Volume of a Box
2011-10-17 03:44
This GeoGebra applet demonstrates the geometric calculation and modeling of a box's volume. Using points, segments, orthogonal lines, and polygons, it explores volume changes and optimization. Originating from a math competition, it helps students intuitively grasp solid geometry, piecewise functions, and definite integrals in volume calculation.
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="4.0" id="930af255-a310-48ff-be2a-f709dc903ff3" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1200" height="769" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.6425" orientation="1" />
</panes>
<views>
<view id="2" visible="false" inframe="false" stylebar="false" location="3,3" size="200" window="0,0,200,400" />
<view id="1" visible="true" inframe="false" stylebar="false" location="3" size="771" window="0,0,400,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="true" inframe="false" stylebar="false" location="1" size="416" window="0,0,400,400" />
<view id="16" visible="false" inframe="true" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" visible="false" inframe="true" stylebar="false" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 39 59 || 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 || 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 || 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 , 14 66 68 | 25 52 60 61 || 40 41 42 , 27 28 35 , 6" />
<input show="true" cmd="true" top="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="12"/>
<graphicsSettings javaLatexFonts="false"/>
<consProtColumns col0="true" col1="true" col2="false" col3="true" col4="false" col5="true" col6="true" col7="false"/>
<consProtocol useColors="true" addIcons="false" showOnlyBreakpoints="false"/>
</gui>
<euclidianView>
<size width="771" height="611"/>
<coordSystem xZero="22.83708309803137" yZero="434.44905993098916" scale="8.886029995776378" yscale="8.886029995776378"/>
<evSettings axes="false" grid="true" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="13" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="10"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<spreadsheetView>
<size width="416" height="611"/>
<prefCellSize width="70" height="24"/>
<spreadsheetColumn id="0" width="128"/>
<spreadsheetColumn id="1" width="161"/>
<spreadsheetColumn id="2" width="116"/>
<selection hScroll="0" vScroll="0" column="-1" row="-1"/>
<layout showFormulaBar="false" showGrid="true" showHScrollBar="true" showVScrollBar="true" showBrowserPanel="false" showColumnHeader="true" showRowHeader ="true" allowSpecialEditor="false" allowToolTips="true" equalsRequired="false"/>
</spreadsheetView>
<kernel>
<continuous val="false"/>
<decimals val="1"/>
<angleUnit val="degree"/>
<algebraStyle val="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="OOO" author="1" date="">
<expression label ="f" exp="f(x) = (30 - 2 * x) * (30 - 2 * x) * x + 0.2103580279319388"/>
<element type="function" label="f">
<show object="true" label="false"/>
<objColor r="255" g="255" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<element type="numeric" label="a">
<value val="0.0"/>
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.1"/>
<layer val="0"/>
<labelOffset x="-3" y="4"/>
<labelMode val="1"/>
<slider min="0" max="15" absoluteScreenLocation="true" width="100.0" x="411.0" y="498.0" fixed="false" horizontal="true"/>
<lineStyle thickness="8" type="15" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<expression label="記錄點" exp="(a, f(a))" type="point" />
<element type="point" label="記錄點">
<show object="true" label="true"/>
<objColor r="64" g="64" b="64" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.2103580279319388" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="A">
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="16.305961067628232" y="-0.10365112165695842" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="Circle[A, 30]"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="46.30596106762823" y="-0.10365112165695842" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="A" a1="B"/>
<output a0="b"/>
</command>
<element type="segment" label="b">
<show object="false" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="30.0" z="3.1095336497087525"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="Circle[A, 30]"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="16.305961067628235" y="29.89634887834304" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="A" a1="C"/>
<output a0="c"/>
</command>
<element type="segment" label="c">
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-30.0" y="3.552713678800501E-15" z="489.17883202884695"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="OrthogonalLine">
<input a0="C" a1="c"/>
<output a0="d"/>
</command>
<element type="line" label="d">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.552713678800501E-15" y="-30.0" z="896.8904663502914"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="OrthogonalLine">
<input a0="B" a1="b"/>
<output a0="e"/>
</command>
<element type="line" label="e">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-30.0" y="0.0" z="1389.178832028847"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="d" a1="e"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="false" label="true"/>
<objColor r="64" g="64" b="64" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="41675.36496086541" y="26906.71399050874" z="900.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="C" a1="D"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="false" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.552713678800501E-15" y="29.999999999999996" z="-896.890466350291"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="D" a1="B"/>
<output a0="h"/>
</command>
<element type="segment" label="h">
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="30.000000000000004" y="0.0" z="-1389.178832028847"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Circle">
<input a0="A" a1="a"/>
<output a0="k"/>
</command>
<element type="conic" label="k">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="265.89510989402834" A3="0.0" A4="-16.305961067628232" A5="0.10365112165695842"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="k" a1="b" a2="1"/>
<output a0="E"/>
</command>
<element type="point" label="E">
<show object="false" label="true"/>
<objColor r="64" g="64" b="64" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="16.305961067628232" y="-0.10365112165695842" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="k" a1="c" a2="1"/>
<output a0="F"/>
</command>
<element type="point" label="F">
<show object="false" label="true"/>
<objColor r="64" g="64" b="64" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="16.305961067628232" y="-0.10365112165695842" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="F" a1="A"/>
<output a0="i"/>
</command>
<element type="segment" label="i">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="A" a1="E"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="OrthogonalLine">
<input a0="F" a1="c"/>
<output a0="l"/>
</command>
<element type="line" label="l">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.552713678800501E-15" y="-30.0" z="-3.1095336497086947"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="OrthogonalLine">
<input a0="E" a1="b"/>
<output a0="m"/>
</command>
<element type="line" label="m">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-30.0" y="0.0" z="489.17883202884695"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="l" a1="m"/>
<output a0="G"/>
</command>
<element type="point" label="G">
<show object="false" label="true"/>
<objColor r="64" g="64" b="64" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="14675.364960865409" y="-93.28600949126258" z="900.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="F" a1="G"/>
<output a0="n"/>
</command>
<element type="segment" label="n">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="G" a1="E"/>
<output a0="p"/>
</command>
<element type="segment" label="p">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Circle">
<input a0="C" a1="a"/>
<output a0="q"/>
</command>
<element type="conic" label="q">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="1159.6760425946109" A3="0.0" A4="-16.305961067628235" A5="-29.89634887834304"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="q" a1="g" a2="1"/>
<output a0="H"/>
</command>
<element type="point" label="H">
<show object="false" label="true"/>
<objColor r="64" g="64" b="64" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="16.305961067628235" y="29.89634887834304" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="q" a1="c" a2="1"/>
<output a0="I"/>
</command>
<element type="point" label="I">
<show object="false" label="true"/>
<objColor r="64" g="64" b="64" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="16.305961067628235" y="29.89634887834304" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="D" a1="a"/>
<output a0="r"/>
</command>
<element type="conic" label="r">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="3038.0337066523048" A3="0.0" A4="-46.30596106762823" A5="-29.896348878343044"/>
<eqnStyle style="specific"/>
</element>
<command name="Circle">
<input a0="B" a1="a"/>
<output a0="s"/>
</command>
<element type="conic" label="s">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="2144.2527739517222" A3="0.0" A4="-46.30596106762823" A5="0.10365112165695842"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="s" a1="b" a2="1"/>
<output a0="J"/>
</command>
<element type="point" label="J">
<show object="false" label="true"/>
<objColor r="64" g="64" b="64" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="46.30596106762823" y="-0.10365112165695842" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="s" a1="h" a2="1"/>
<output a0="K"/>
</command>
<element type="point" label="K">
<show object="false" label="true"/>
<objColor r="64" g="64" b="64" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="46.30596106762823" y="-0.10365112165695842" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="r" a1="h" a2="1"/>
<output a0="L"/>
</command>
<element type="point" label="L">
<show object="false" label="true"/>
<objColor r="64" g="64" b="64" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="46.305961067628225" y="29.896348878343044" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="r" a1="g" a2="1"/>
<output a0="M"/>
</command>
<element type="point" label="M">
<show object="false" label="true"/>
<objColor r="64" g="64" b="64" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="46.30596106762823" y="29.896348878343044" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="C" a1="H"/>
<output a0="t"/>
</command>
<element type="segment" label="t">
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C" a1="I"/>
<output a0="a_1"/>
</command>
<element type="segment" label="a_1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="M" a1="D"/>
<output a0="b_1"/>
</command>
<element type="segment" label="b_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="D" a1="L"/>
<output a0="c_1"/>
</command>
<element type="segment" label="c_1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-7.105427357601002E-15" z="2.2737367544323206E-13"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="K" a1="B"/>
<output a0="d_1"/>
</command>
<element type="segment" label="d_1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B" a1="J"/>
<output a0="e_1"/>
</command>
<element type="segment" label="e_1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="OrthogonalLine">
<input a0="I" a1="c"/>
<output a0="f_1"/>
</command>
<element type="line" label="f_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.552713678800501E-15" y="-30.0" z="896.8904663502914"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="OrthogonalLine">
<input a0="M" a1="g"/>
<output a0="g_1"/>
</command>
<element type="line" label="g_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-29.999999999999996" y="-3.552713678800501E-15" z="1389.1788320288467"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="m" a1="f_1"/>
<output a0="N"/>
</command>
<element type="point" label="N">
<show object="false" label="true"/>
<objColor r="64" g="64" b="64" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="14675.364960865409" y="26906.713990508742" z="900.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="f_1" a1="g_1"/>
<output a0="O"/>
</command>
<element type="point" label="O">
<show object="false" label="true"/>
<objColor r="64" g="64" b="64" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="41675.3649608654" y="26906.713990508735" z="899.9999999999999"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="l" a1="g_1"/>
<output a0="Q"/>
</command>
<element type="point" label="Q">
<show object="false" label="true"/>
<objColor r="64" g="64" b="64" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="41675.3649608654" y="-93.28600949126576" z="899.9999999999999"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="I" a1="N"/>
<output a0="h_1"/>
</command>
<element type="segment" label="h_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-7.105427357601002E-15" y="-3.552713678800501E-15" z="2.2737367544323206E-13"/>
<lineStyle thickness="2" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="N" a1="H"/>
<output a0="i_1"/>
</command>
<element type="segment" label="i_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7.105427357601002E-15" y="3.552713678800501E-15" z="-2.2737367544323206E-13"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="M" a1="O"/>
<output a0="j_1"/>
</command>
<element type="segment" label="j_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="O" a1="L"/>
<output a0="k_1"/>
</command>
<element type="segment" label="k_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-7.105427357601002E-15" z="2.2737367544323206E-13"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="K" a1="Q"/>
<output a0="l_1"/>
</command>
<element type="segment" label="l_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.552713678800501E-15" y="0.0" z="-1.6431300764452317E-13"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="Q" a1="J"/>
<output a0="m_1"/>
</command>
<element type="segment" label="m_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.552713678800501E-15" y="0.0" z="1.6431300764452317E-13"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="N" a1="O"/>
<output a0="n_1"/>
</command>
<element type="segment" label="n_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.552713678800501E-15" y="30.0" z="-896.8904663502915"/>
<lineStyle thickness="2" type="20" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="O" a1="Q"/>
<output a0="p_1"/>
</command>
<element type="segment" label="p_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="30.000000000000007" y="0.0" z="-1389.1788320288472"/>
<lineStyle thickness="2" type="20" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="Q" a1="G"/>
<output a0="q_1"/>
</command>
<element type="segment" label="q_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.552713678800501E-15" y="-30.0" z="-3.1095336497086947"/>
<lineStyle thickness="2" type="20" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="G" a1="N"/>
<output a0="r_1"/>
</command>
<element type="segment" label="r_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-30.000000000000007" y="0.0" z="489.17883202884707"/>
<lineStyle thickness="2" type="20" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="N" a1="O" a2="Q" a3="G"/>
<output a0="Poly1" a1="n_2" a2="o" a3="q_2" a4="g_2"/>
</command>
<element type="polygon" label="Poly1">
<lineStyle thickness="8" type="20" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="0" g="51" b="153" alpha="0.6"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="n_2">
<show object="false" label="false"/>
<objColor r="0" g="51" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.552713678800501E-15" y="30.0" z="-896.8904663502915"/>
<lineStyle thickness="8" type="20" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="o">
<show object="false" label="false"/>
<objColor r="0" g="51" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="30.000000000000007" y="0.0" z="-1389.1788320288472"/>
<lineStyle thickness="8" type="20" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="q_2">
<show object="false" label="false"/>
<objColor r="0" g="51" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.552713678800501E-15" y="-30.0" z="-3.1095336497086947"/>
<lineStyle thickness="8" type="20" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="g_2">
<show object="false" label="false"/>
<objColor r="0" g="51" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-30.000000000000007" y="0.0" z="489.17883202884707"/>
<lineStyle thickness="8" type="20" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="M" a1="O" a2="L" a3="D"/>
<output a0="多邊形2" a1="m_2" a2="o_1" a3="l_2" a4="d_2"/>
</command>
<element type="polygon" label="多邊形2">
<lineStyle thickness="8" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="m_2">
<show object="false" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="o_1">
<show object="false" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-7.105427357601002E-15" z="2.2737367544323206E-13"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="l_2">
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="7.105427357601002E-15" z="-2.2737367544323206E-13"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="d_2">
<show object="false" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="Q" a1="K" a2="B" a3="J"/>
<output a0="多邊形3" a1="q_3" a2="k_2" a3="b_2" a4="j_2"/>
</command>
<element type="polygon" label="多邊形3">
<lineStyle thickness="8" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="q_3">
<show object="false" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.552713678800501E-15" y="0.0" z="1.6431300764452317E-13"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="k_2">
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="b_2">
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="j_2">
<show object="false" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.552713678800501E-15" y="0.0" z="-1.6431300764452317E-13"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="F" a1="G" a2="E" a3="A"/>
<output a0="多邊形4" a1="f_2" a2="g_3" a3="e_2" a4="a_2"/>
</command>
<element type="polygon" label="多邊形4">
<lineStyle thickness="8" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="f_2">
<show object="false" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="g_3">
<show object="false" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="e_2">
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="a_2">
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="C" a1="H" a2="N" a3="I"/>
<output a0="多邊形5" a1="c_2" a2="h_2" a3="n_3" a4="i_2"/>
</command>
<element type="polygon" label="多邊形5">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="c_2">
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="h_2">
<show object="false" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-7.105427357601002E-15" y="-3.552713678800501E-15" z="2.2737367544323206E-13"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="n_3">
<show object="false" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7.105427357601002E-15" y="3.552713678800501E-15" z="-2.2737367544323206E-13"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="i_2">
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="H" a1="M" a2="O" a3="N"/>
<output a0="多邊形6" a1="h_3" a2="m_3" a3="o_2" a4="n_4"/>
</command>
<element type="polygon" label="多邊形6">
<lineStyle thickness="8" type="20" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="h_3">
<show object="false" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.552713678800501E-15" y="29.999999999999996" z="-896.890466350291"/>
<lineStyle thickness="8" type="20" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="m_3">
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="8" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="o_2">
<show object="true" label="false"/>
<objColor r="0" g="51" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.552713678800501E-15" y="-30.0" z="896.8904663502915"/>
<lineStyle thickness="8" type="20" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="n_4">
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7.105427357601002E-15" y="3.552713678800501E-15" z="-2.2737367544323206E-13"/>
<lineStyle thickness="8" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="O" a1="L" a2="K" a3="Q"/>
<output a0="多邊形7" a1="o_3" a2="l_3" a3="k_3" a4="q_4"/>
</command>
<element type="polygon" label="多邊形7">
<lineStyle thickness="8" type="20" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="o_3">
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-7.105427357601002E-15" z="2.2737367544323206E-13"/>
<lineStyle thickness="8" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="l_3">
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="30.000000000000004" y="7.105427357601002E-15" z="-1389.178832028847"/>
<lineStyle thickness="8" type="20" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="k_3">
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.552713678800501E-15" y="0.0" z="-1.6431300764452317E-13"/>
<lineStyle thickness="8" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="q_4">
<show object="true" label="false"/>
<objColor r="0" g="51" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-30.000000000000007" y="0.0" z="1389.1788320288472"/>
<lineStyle thickness="8" type="20" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="G" a1="Q" a2="J" a3="E"/>
<output a0="多邊形8" a1="g_4" a2="q_5" a3="j_3" a4="e_3"/>
</command>
<element type="polygon" label="多邊形8">
<lineStyle thickness="8" type="20" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="g_4">
<show object="true" label="false"/>
<objColor r="0" g="51" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.552713678800501E-15" y="30.0" z="3.1095336497086947"/>
<lineStyle thickness="8" type="20" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="q_5">
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.552713678800501E-15" y="0.0" z="1.6431300764452317E-13"/>
<lineStyle thickness="8" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="j_3">
<show object="false" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-30.0" z="-3.1095336497087525"/>
<lineStyle thickness="8" type="20" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="e_3">
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="8" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Polygon">
<input a0="I" a1="N" a2="G" a3="F"/>
<output a0="多邊形9" a1="i_3" a2="n_5" a3="g_5" a4="f_3"/>
</command>
<element type="polygon" label="多邊形9">
<lineStyle thickness="8" type="20" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.25"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="i_3">
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-7.105427357601002E-15" y="-3.552713678800501E-15" z="2.2737367544323206E-13"/>
<lineStyle thickness="8" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="n_5">
<show object="true" label="false"/>
<objColor r="0" g="51" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="30.000000000000007" y="0.0" z="-489.17883202884707"/>
<lineStyle thickness="8" type="20" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="g_5">
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="0.0" z="0.0"/>
<lineStyle thickness="8" type="15" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="f_3">
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-30.0" y="3.552713678800501E-15" z="489.17883202884695"/>
<lineStyle thickness="8" type="20" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="文字1" exp=""小正方形的邊長 =""/>
<element type="text" label="文字1">
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" size="6" style="1"/>
<startPoint x="10.627607572991366" y="-8.077767034570687" z="1.0"/>
</element>
<expression label="文字3" exp=""盒子的底面積 = ""/>
<element type="text" label="文字3">
<show object="true" label="false"/>
<objColor r="0" g="51" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" size="6" style="1"/>
<startPoint x="12.837380676684003" y="-12.157052261198755" z="1.0"/>
</element>
<expression label="文字4" exp="Poly1 + """ />
<element type="text" label="文字4">
<show object="true" label="false"/>
<objColor r="0" g="51" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" size="6" style="1"/>
<startPoint x="29.435623244533648" y="-12.575352280241205" z="1.0"/>
</element>
<expression label="文字5" exp="Poly1 * a_2 + """ />
<element type="text" label="文字5">
<show object="true" label="false"/>
<objColor r="255" g="0" b="102" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" size="6" style="1"/>
<startPoint x="28.991153892543284" y="-15.980045116248702" z="1.0"/>
</element>
<expression label="文字6" exp=""盒子的體積 = ""/>
<element type="text" label="文字6">
<show object="true" label="false"/>
<objColor r="255" g="0" b="102" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" size="6" style="1"/>
<startPoint x="14.816523712863443" y="-16.107295671837864" z="1.0"/>
</element>
<expression label="文字7" exp=""cm""/>
<element type="text" label="文字7">
<show object="true" label="false"/>
<objColor r="51" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" size="6" style="1"/>
<startPoint x="36.99897658315136" y="-7.774438584167655" z="1.0"/>
</element>
<expression label="文字8" exp=""cm³""/>
<element type="text" label="文字8">
<show object="true" label="false"/>
<objColor r="255" g="0" b="102" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" size="6" style="1"/>
<startPoint x="37.30765317639607" y="-15.642436532727611" z="1.0"/>
</element>
<expression label="文字9" exp="a_2 + """ />
<element type="text" label="文字9">
<show object="true" label="false"/>
<objColor r="102" g="153" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" size="6" style="1"/>
<startPoint x="30.09176907771146" y="-8.09733280660662" z="1.0"/>
</element>
<expression label="文字10" exp=""cm²""/>
<element type="text" label="文字10">
<show object="true" label="false"/>
<objColor r="0" g="51" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" size="6" style="1"/>
<startPoint x="37.16620927495268" y="-12.053513808395959" z="1.0"/>
</element>
<command name="Segment">
<input a0="C" a1="D"/>
<output a0="s_1"/>
</command>
<element type="segment" label="s_1">
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-3.552713678800501E-15" y="29.999999999999996" z="-896.890466350291"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="E" a1="J"/>
<output a0="t_1"/>
</command>
<element type="segment" label="t_1">
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="30.0" z="3.1095336497087525"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="P">
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="50.0" y="30.0" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="6"/>
</element>
<command name="Point">
<input a0="xAxis"/>
<output a0="V"/>
</command>
<element type="point" label="V">
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="50.0" y="0.0" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="7"/>
</element>
<command name="Segment">
<input a0="P" a1="V"/>
<output a0="a_3"/>
</command>
<element type="segment" label="a_3">
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="24" y="-13"/>
<labelMode val="2"/>
<coords x="30.0" y="0.0" z="-1500.0"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="文字11" exp=""30cm""/>
<element type="text" label="文字11">
<show object="true" label="false"/>
<objColor r="51" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" size="6" style="0"/>
<startPoint x="51.32617743374628" y="14.765267558929477" z="1.0"/>
</element>
<element type="point" label="W">
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="16.599426567902963" y="-2.6470187907046383" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="9"/>
</element>
<command name="Point">
<input a0="Circle[W, a_3]"/>
<output a0="Z"/>
</command>
<element type="point" label="Z">
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="46.59942656790297" y="-2.6470187907046383" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="8"/>
</element>
<command name="Segment">
<input a0="W" a1="Z"/>
<output a0="b_3"/>
</command>
<element type="segment" label="b_3">
<show object="true" label="false"/>
<objColor r="153" g="153" b="153" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="30.000000000000004" z="79.41056372113916"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="文字12" exp=""30cm""/>
<element type="text" label="文字12">
<show object="true" label="false"/>
<objColor r="51" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" size="6" style="0"/>
<startPoint x="27.946759245192606" y="-4.799099126052675" z="1.0"/>
</element>
<element type="point" label="R">
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="10.034055359294161" y="-5.238665646091334" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="S">
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="56.51150369069786" y="-5.351201840598365" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="T">
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="56.62403988520489" y="-17.842719430878777" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="U">
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="10.034055359294161" y="-17.842719430878777" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="R" a1="S" a2="T" a3="U"/>
<output a0="多邊形1" a1="r_2" a2="s_2" a3="t_2" a4="u"/>
</command>
<element type="polygon" label="多邊形1">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="r_2">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.11253619450703045" y="46.47744833140369" z="242.35061748610173"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="s_2">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="12.491517590280413" y="0.11253619450702956" z="-705.3122385143688"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="t_2">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-46.58998452591072" z="-831.2920221848088"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="u">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-12.604053784787443" y="0.0" z="126.4697734280783"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="image" label="圖片1">
<file name="87484f25cb13bc9251c78a66c72f62a2\king.bmp"/>
<inBackground val="false"/>
<startPoint number="0" exp="A_1"/>
<startPoint number="1" exp="B_1"/>
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<element type="point" label="A_1">
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="55.04853316210646" y="29.309946067567104" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="B_1">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-67" y="-43"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="65.51439925126031" y="30.660380401651473" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="文字2" exp=""國王給了小天使一張30cm x 30cm的正方形卡紙：""/>
<element type="text" label="文字2">
<show object="true" label="false"/>
<objColor r="0" g="153" b="204" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" size="6" style="1"/>
<startPoint x="0.13087024267545644" y="41.12624649080533" z="1.0"/>
</element>
<expression label="文字13" exp=""你能找出盒子的最大體積嗎 ?""/>
<element type="text" label="文字13">
<show object="true" label="true"/>
<objColor r="255" g="0" b="102" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" size="6" style="1"/>
<startPoint x="9.696446775773065" y="35.38690057094676" z="1.0"/>
</element>
<element type="image" label="pic1">
<file name="1779248989f1421df35aaefb33af1dd8\tips start.bmp"/>
<inBackground val="false"/>
<startPoint number="0" x="-3.77384120577646" y="-2.905963637960136" z="1.0"/>
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="v">
<value val="0.0"/>
<show object="true" label="false"/>
<objColor r="0" g="153" b="51" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="1" absoluteScreenLocation="true" width="100.0" x="576.0" y="499.0" fixed="false" horizontal="true"/>
<lineStyle thickness="9" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="text1" exp=""答案棒""/>
<element type="text" label="text1">
<show object="true" label="false"/>
<objColor r="0" g="153" b="51" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" size="6" style="1"/>
<startPoint x="61.23802385999314" y="-5.013593257077274" z="1.0"/>
</element>
<expression label="text2" exp=""當小正方形的邊長是5cm時, 就是該盒子的最大體積, 也就是約2000cm³。""/>
<element type="text" label="text2">
<show object="true" label="false"/>
<condition showObject="v ≟ 1"/>
<objColor r="0" g="153" b="51" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" size="6" style="1"/>
<startPoint x="62.36338580506346" y="-10.64040298242881" z="1.0"/>
</element>
<expression label="text3" exp=""MTH 2101, Carol Chan C.K., HKIEd""/>
<element type="text" label="text3">
<show object="true" label="false"/>
<objColor r="102" g="102" b="102" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<startPoint x="61.57563244351424" y="-16.60482129130144" z="1.0"/>
</element>
</construction>
</geogebra>