体积测量（二）：立方体构造与平移变换
2016-05-06 04:26
本 GeoGebra 范例演示如何利用 Cube（立方体）与 Translate（平移）命令在三维空间中构造几何体并测量其体积。通过定义空间关键点（A、B、C 等）及方向向量（s100、s010、s001），逐步构建包含多个面（face）与棱（edge）的立方体模型，帮助学习者直观理解立体几何中体积的概念、空间坐标系的运用以及平移变换在三维建模中的作用。适用于中学及大学阶段的立体几何教学与探究。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.238.0" id="d3da4afc-dd06-40b5-a85b-0e93380c2252" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="903" height="551" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.19419237749546278" orientation="0" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1,1" size="400" window="364,216,953,569" />
<view id="1" visible="false" inframe="false" stylebar="false" location="0,0" size="100" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="true" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="2" visible="false" inframe="true" stylebar="true" location="3" size="174" window="684,132,312,738" />
<view id="16" visible="true" inframe="false" stylebar="false" location="0" size="107" window="660,284,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="true" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="true" inframe="false" stylebar="false" location="2" size="434" window="100,100,600,400" />
</views>
<toolbar show="false" items="0 39 | 1 501 67 , 5 19 , 72 75 76 | 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 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="20"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="900" height="548"/>
<coordSystem xZero="203.99999999999997" yZero="320.0000000000001" scale="49.99999999999999" yscale="50.000000000000014"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" 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="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="900" height="106"/>
<coordSystem xZero="215.00000000000003" yZero="320.0000000000008" scale="50.00000000000001" yscale="50.00000000000016"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="2" rightAngleStyle="1" checkboxSize="26" 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="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<grid distX="0.1" distY="0.1" distTheta="0.5235987755982988"/>
</euclidianView>
<kernel>
<uses3D val="true"/>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<euclidianView3D>
<coordSystem xZero="0.1370021200400217" yZero="-0.16068592632118223" zZero="-1.2344972953241042" scale="61.08268938689645" xAngle="19" zAngle="-45.6909366756378"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" gridType="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="2" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<plate show="false"/>
<bgColor r="255" g="255" b="255"/>
<clipping use="false" show="false" size="1"/>
<projection type="0"/>
</euclidianView3D>
<construction title="" author="" date="">
<element type="point3d" label="A">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="-4" y="1" z="0" w="1"/>
<pointSize val="5"/>
</element>
<element type="point3d" label="B">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="-3" y="1" z="0" w="1"/>
<pointSize val="5"/>
</element>
<command name="Point">
<input a0="Circle[B, Distance[A, B], Segment[A, B]]"/>
<output a0="C"/>
</command>
<element type="point3d" label="C">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="-3" y="2" z="0" w="1"/>
<pointSize val="5"/>
</element>
<element type="point3d" label="I">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="-4" y="0" z="0" w="1"/>
<pointSize val="5"/>
</element>
<element type="point3d" label="J">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="-3" y="0" z="0" w="1"/>
<pointSize val="5"/>
</element>
<command name="Point">
<input a0="Circle[J, Distance[I, J], Segment[I, J]]"/>
<output a0="K"/>
</command>
<element type="point3d" label="K">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="-3" y="1" z="0" w="1"/>
<pointSize val="5"/>
</element>
<element type="point3d" label="Q">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="-2" y="1" z="0" w="1"/>
<pointSize val="5"/>
</element>
<element type="point3d" label="R">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="-2" y="2" z="0" w="1"/>
<pointSize val="5"/>
</element>
<command name="Point">
<input a0="Circle[R, Distance[Q, R], Segment[Q, R]]"/>
<output a0="S"/>
</command>
<element type="point3d" label="S">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="-3" y="2" z="-1.2246467991473532e-16" w="1"/>
<pointSize val="5"/>
</element>
<element type="point3d" label="G_1">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="1" y="1" z="0" w="1"/>
<pointSize val="5"/>
</element>
<element type="point3d" label="H_1">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="2" y="1" z="0" w="1"/>
<pointSize val="5"/>
</element>
<command name="Point">
<input a0="Circle[H_1, Distance[G_1, H_1], Segment[G_1, H_1]]"/>
<output a0="I_1"/>
</command>
<element type="point3d" label="I_1">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="2" y="2" z="0" w="1"/>
<pointSize val="5"/>
</element>
<command name="Cube">
<input a0="G_1" a1="H_1" a2="I_1"/>
<output a0="e_1" a1="J_1" a2="K_1" a3="L_1" a4="M_1" a5="N_1" a6="face7" a7="face9" a8="facey" a9="facex" a10="face11" a11="facez" a12="edge13" a13="edge12" a14="edge15" a15="edge17" a16="edge14" a17="edge19" a18="edge21" a19="edge20" a20="edge16" a21="edge22" a22="edge18" a23="edge23"/>
</command>
<element type="polyhedron" label="e_1">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false" ev="4"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="point3d" label="J_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1" y="2" z="0" w="1"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="K_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1" y="1" z="1" w="1"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="L_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2" y="1" z="1" w="1"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="M_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2" y="2" z="1" w="1"/>
<pointSize val="3"/>
</element>
<element type="point3d" label="N_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1" y="2" z="1" w="1"/>
<pointSize val="3"/>
</element>
<element type="polygon3d" label="face7">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false" ev="4"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="face9">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false" ev="4"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="facey">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="(¬s010) ∧ vol"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<ggbscript val="SetValue[s010, !s010]"/>
</element>
<element type="polygon3d" label="facex">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="(¬s100) ∧ vol"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<ggbscript val="SetValue[s100, !s100]"/>
</element>
<element type="polygon3d" label="face11">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false" ev="4"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
</element>
<element type="polygon3d" label="facez">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="(¬s001) ∧ vol"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="1"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<ggbscript val="SetValue[s001, !s001]"/>
</element>
<element type="segment3d" label="edge13">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="192" b="203" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge12">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="192" b="203" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge15">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="192" b="203" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge17">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="192" b="203" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge14">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="192" b="203" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge19">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="192" b="203" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge21">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="192" b="203" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge20">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="192" b="203" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge16">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="192" b="203" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge22">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="192" b="203" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge18">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="192" b="203" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="edge23">
<show object="false" label="false" ev="4"/>
<objColor r="255" g="192" b="203" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Translate">
<input a0="Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]]" a1="Vector[(0, 0), (2, 1)]"/>
<output a0="f"/>
</command>
<element type="polyhedron" label="f">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="s100"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<expression label ="s100" exp="false"/>
<element type="boolean" label="s100">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label ="s010" exp="false"/>
<element type="boolean" label="s010">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label ="s001" exp="false"/>
<element type="boolean" label="s001">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<command name="Translate">
<input a0="Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]]" a1="Vector[(0, 0), (1, 0)]"/>
<output a0="g"/>
</command>
<element type="polyhedron" label="g">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="s010"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Translate">
<input a0="Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]]" a1="Vector[(0, 0), (1, 1, 1)]"/>
<output a0="h"/>
</command>
<element type="polyhedron" label="h">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="s001"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Translate">
<input a0="Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]]" a1="Vector[(0, 0), (1, 1)]"/>
<output a0="e"/>
</command>
<element type="polyhedron" label="e">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="vol"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Translate">
<input a0="Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]]" a1="Vector[(0, 0), (1, 1)]"/>
<output a0="e'"/>
</command>
<element type="polyhedron" label="e'">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="vol"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Translate">
<input a0="facex" a1="Vector[(0, 0, 0), (0, -1, 0)]"/>
<output a0="facex010"/>
</command>
<element type="polygon3d" label="facex010">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="s010 ∧ (¬x010)"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="1"/>
<labelMode val="0"/>
<ggbscript val="SetValue[x010, !x010] SetValue[y100, !y100]"/>
</element>
<command name="Translate">
<input a0="facey" a1="Vector[(0, 0), (1, 0, 0)]"/>
<output a0="facey100"/>
</command>
<element type="polygon3d" label="facey100">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="s100 ∧ (¬y100)"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="1"/>
<labelMode val="0"/>
<ggbscript val="SetValue[y100, !y100] SetValue[x010, !x010]"/>
</element>
<expression label ="x010" exp="false"/>
<element type="boolean" label="x010">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label ="y100" exp="false"/>
<element type="boolean" label="y100">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<command name="Translate">
<input a0="Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]]" a1="Vector[(0, 0), (2, 1)]"/>
<output a0="f'"/>
</command>
<element type="polyhedron" label="f'">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="s100"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Translate">
<input a0="Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]]" a1="Vector[(2, 0)]"/>
<output a0="a"/>
</command>
<element type="polyhedron" label="a">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="x010 ∨ y100"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Translate">
<input a0="Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]]" a1="Vector[(2, 0)]"/>
<output a0="a'"/>
</command>
<element type="polyhedron" label="a'">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="x010 ∨ y100"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Translate">
<input a0="facez" a1="Vector[(0, 0, 0), (0, -1, 0)]"/>
<output a0="facez010"/>
</command>
<element type="polygon3d" label="facez010">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="s010 ∧ (¬z010)"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="1"/>
<labelMode val="0"/>
<ggbscript val="SetValue[z010, !z010] SetValue[y001, !y001]"/>
</element>
<command name="Translate">
<input a0="facey" a1="Vector[(0, 0, 1)]"/>
<output a0="facey001"/>
</command>
<element type="polygon3d" label="facey001">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="s001 ∧ (¬y001)"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="1"/>
<labelMode val="0"/>
<ggbscript val="SetValue[y001, !y001] SetValue[z010, !z010]"/>
</element>
<expression label ="z010" exp="false"/>
<element type="boolean" label="z010">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label ="y001" exp="false"/>
<element type="boolean" label="y001">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<command name="Translate">
<input a0="Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]]" a1="Vector[(1, 0, 1)]"/>
<output a0="b"/>
</command>
<element type="polyhedron" label="b">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="z010 ∨ y001"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Translate">
<input a0="Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]]" a1="Vector[(1, 0, 1)]"/>
<output a0="b'"/>
</command>
<element type="polyhedron" label="b'">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false" ev="4"/>
<condition showObject="z010 ∨ y001"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Translate">
<input a0="Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]]" a1="Vector[(0, 0), (1, 0)]"/>
<output a0="g'"/>
</command>
<element type="polyhedron" label="g'">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="s010"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Translate">
<input a0="Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]]" a1="Vector[(0, 0), (1, 1, 1)]"/>
<output a0="h'"/>
</command>
<element type="polyhedron" label="h'">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="s001"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<element type="button" label="button1">
<show object="true" label="true" ev="3"/>
<condition showObject="vol"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelOffset x="814" y="68"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[s001, false] SetValue[s010, false] SetValue[s100, false] SetValue[x010, false] SetValue[y001, false] SetValue[y100, false] SetValue[z010, false] SetValue[vol, false]"/>
<font serif="false" sizeM="2" size="20" style="0"/>
<caption val="Reset"/>
</element>
<element type="boolean" label="vol">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<condition showObject="¬vol"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="780" y="10"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="Volume"/>
</element>
<command name="Translate">
<input a0="Prism[Polygon[(-4, 2), (-2, 2), (-2, 2, 1), (-3, 2, 1), (-3, 2, 2), (-4, 2, 2)], (-4, 0, 0)]" a1="Vector[(0, 0)]"/>
<output a0="c"/>
</command>
<element type="polyhedron" label="c">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="153" g="204" b="255" alpha="1"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Translate">
<input a0="Prism[Polygon[(-4, 2), (-2, 2), (-2, 2, 1), (-3, 2, 1), (-3, 2, 2), (-4, 2, 2)], (-4, 0, 0)]" a1="Vector[(0, 0)]"/>
<output a0="d"/>
</command>
<element type="polyhedron" label="d">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Translate">
<input a0="Polygon[(-4, 1), (-2, 1), (-2, 1, 1), (-3, 1, 1), (-3, 1, 2), (-4, 1, 2)]" a1="Vector[(0, 0)]"/>
<output a0="poly1"/>
</command>
<element type="polygon3d" label="poly1">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Translate">
<input a0="Polygon[(-4, 0, 1), (-3, 0, 1), (-3, 2, 1), (-4, 2, 1)]" a1="Vector[(0, 0)]"/>
<output a0="poly2"/>
</command>
<element type="polygon3d" label="poly2">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Translate">
<input a0="Polygon[(-3, 0, 0), (-3, 2, 0), (-3, 2, 1), (-3, 0, 1)]" a1="Vector[(0, 0)]"/>
<output a0="poly3"/>
</command>
<element type="polygon3d" label="poly3">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<expression label="text2" exp=""\text{Construct a copy of the blue model by clicking on the faces of the red blocks. \\Fnd its volume.}""/>
<element type="text" label="text2">
<show object="false" label="false" ev="11"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="0"/>
<startPoint x="-2.5499999999999967" y="5.3300000000000045" z="1"/>
</element>
<expression label="text4" exp=""\text{The model is made of cubic centimeter blocks. What is its volume?}""/>
<element type="text" label="text4">
<show object="false" label="false" ev="11"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="0"/>
<startPoint x="4.550000000000001" y="5.130000000000003" z="1"/>
</element>
<expression label="text1" exp=""" + (LaTeX[If[vol, text2, text4]]) + """ />
<element type="text" label="text1">
<show object="true" label="false" ev="11"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="8" y="8"/>
</element>
<expression label="text3" exp=""\Large\text{The volume of the model is:\;\;}\fgcolor{red}\text{" + (LaTeX[s001 + s010 + s100 + (x010 * y100) + (y001 * z010) + 1]) + "\;cm^3}"" />
<element type="text" label="text3">
<show object="true" label="false" ev="11"/>
<condition showObject="vol"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="218" y="58"/>
</element>
<element type="point3d" label="D">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="-5" y="5" z="0" w="1"/>
<pointSize val="5"/>
</element>
<element type="point3d" label="E">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="-5" y="-4" z="0" w="1"/>
<pointSize val="5"/>
</element>
<element type="point3d" label="F">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="5" y="-4" z="0" w="1"/>
<pointSize val="5"/>
</element>
<element type="point3d" label="G">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="5" y="5" z="0" w="1"/>
<pointSize val="5"/>
</element>
</construction>
</geogebra>