长方体的体积
2017-08-28 18:38
本范例演示了如何计算和可视化长方体的体积。通过调整长方体的长、宽、高,用户可以直观地观察长方体形状的变化,并理解体积公式的几何意义。范例中使用了平移、向量和序列等命令来构建长方体及其内部结构,帮助学习者深入理解立体几何中体积的概念与计算方法。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.236.0" id="8ec7443a-200b-4e5b-8bee-60c87c7395f1" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="969" height="533" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.6153846153846154" orientation="0" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1,1" size="400" window="189,235,981,725" />
<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="1" visible="false" inframe="false" stylebar="false" location="0" size="100" window="100,100,600,400" />
<view id="2" visible="false" inframe="true" stylebar="true" location="3" size="174" window="1332,193,299,749" />
<view id="16" visible="true" inframe="false" stylebar="false" location="2" size="195" 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="0" size="328" 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="968" height="530"/>
<coordSystem xZero="205" yZero="318.9999999999999" scale="49.999999999999986" yscale="49.99999999999998"/>
<evSettings axes="true" 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="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="968" height="194"/>
<coordSystem xZero="179.0000000000001" yZero="315.00000000000006" scale="50.00000000000002" yscale="50.00000000000002"/>
<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" yZero="0" zZero="-1.5" scale="60.500000000000014" xAngle="14" zAngle="-67.85047534121243"/>
<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="2"/>
<projection type="0"/>
</euclidianView3D>
<construction title="" author="" date="">
<element type="numeric" label="l">
<value val="5"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-5" max="5" absoluteScreenLocation="true" width="200" x="30" y="90" fixed="true" horizontal="true" showAlgebra="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="w">
<value val="4"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-5" max="5" absoluteScreenLocation="true" width="200" x="30" y="130" fixed="true" horizontal="true" showAlgebra="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="h">
<value val="3"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-5" max="5" absoluteScreenLocation="true" width="200" x="30" y="50" fixed="true" horizontal="true" showAlgebra="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<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="1" speed="1" type="0" playing="false"/>
<coords x="-3" y="2" z="0" w="1"/>
<pointSize val="5"/>
</element>
<command name="Translate">
<input a0="Prism[Polygon[A, A + (l, 0), A + (l, (-w)), A + (0, (-w))], (-h)]" a1="Vector[(0, 0)]"/>
<output a0="a"/>
</command>
<element type="polyhedron" label="a">
<lineStyle thickness="4" type="0" typeHidden="2"/>
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
</element>
<element type="numeric" label="l1">
<value val="1"/>
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="l" absoluteScreenLocation="true" width="200" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="w1">
<value val="1"/>
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="w" absoluteScreenLocation="true" width="200" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="h1">
<value val="1"/>
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="h" absoluteScreenLocation="true" width="200" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Vector">
<input a0="(1, 0, 0)"/>
<output a0="u1"/>
</command>
<element type="vector3d" label="u1">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1" y="0" z="0" w="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<expression label ="u2" exp="(0, -1, 0)" type="vector"/>
<element type="vector3d" label="u2">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="0" y="-1" z="0" w="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<expression label ="u3" exp="(0, 0, 1)" type="vector"/>
<element type="vector3d" label="u3">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="0" y="0" z="1" w="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
</element>
<element type="button" label="button1">
<show object="true" label="true" ev="3"/>
<condition showObject="vol"/>
<objColor r="255" g="0" b="0" alpha="1"/>
<layer val="0"/>
<labelOffset x="280" y="75"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[l1, l1+1] SetValue[w1, If[l1!=l, 1, w1]] SetValue[h1, If[l1!=l, 1, h1]]"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<caption val="+"/>
</element>
<element type="button" label="button2">
<show object="true" label="true" ev="3"/>
<condition showObject="vol"/>
<objColor r="255" g="0" b="0" alpha="1"/>
<layer val="0"/>
<labelOffset x="235" y="75"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[l1, l1-1] SetValue[w1, If[l1!=l, 1, w1]] SetValue[h1, If[l1!=l, 1, h1]]"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<caption val="—"/>
</element>
<element type="button" label="button3">
<show object="true" label="true" ev="3"/>
<condition showObject="showrows ∧ vol"/>
<objColor r="0" g="0" b="255" alpha="1"/>
<layer val="0"/>
<labelOffset x="280" y="115"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[w1, w1+1] SetValue[h1, If[w1!=w, 1, h1]]"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<caption val="+"/>
</element>
<element type="button" label="button4">
<show object="true" label="true" ev="3"/>
<condition showObject="showrows ∧ vol"/>
<objColor r="0" g="0" b="255" alpha="1"/>
<layer val="0"/>
<labelOffset x="235" y="115"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[w1, w1-1] SetValue[h1, If[w1!=w, 1, h1]]"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<caption val="—"/>
</element>
<element type="button" label="button5">
<show object="true" label="true" ev="3"/>
<condition showObject="showlayers ∧ vol"/>
<objColor r="0" g="100" b="0" alpha="1"/>
<layer val="0"/>
<labelOffset x="280" y="155"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[h1, h1+1]"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<caption val="+"/>
</element>
<element type="button" label="button6">
<show object="true" label="true" ev="3"/>
<condition showObject="showlayers ∧ vol"/>
<objColor r="0" g="100" b="0" alpha="1"/>
<layer val="0"/>
<labelOffset x="235" y="155"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[h1, h1-1]"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<caption val="—"/>
</element>
<command name="Translate">
<input a0="Prism[Polygon[A, A - (0, 1), A + (1, -1), A + (1, 0)], 1]" a1="Vector[(-1, 1, -1)]"/>
<output a0="b"/>
</command>
<element type="polyhedron" label="b">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false" ev="7"/>
<objColor r="153" g="51" b="0" alpha="0.4"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="If">
<input a0="l1 ≟ l" a1="true"/>
<output a0="showrows"/>
</command>
<element type="boolean" label="showrows">
<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="If">
<input a0="l1 ≟ l ∧ w1 ≟ w" a1="true" a2="false"/>
<output a0="showlayers"/>
</command>
<element type="boolean" label="showlayers">
<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="If">
<input a0="l1 ≟ l ∧ w1 ≟ w ∧ h1 ≟ h" a1="true" a2="false"/>
<output a0="showall"/>
</command>
<element type="boolean" label="showall">
<value val="false"/>
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="text6" exp=""\fgcolor{red} " + (LaTeX[l]) + "\;×\;\fgcolor{blue} " + (LaTeX[w]) + "\;×\;\fgcolor{OliveGreen}" + (LaTeX[h]) + " \;=\; " + (LaTeX[((l * w) * h)]) + "(\text{cm^3})"" />
<element type="text" label="text6">
<show object="false" label="false" ev="11"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="472" y="98"/>
</element>
<element type="boolean" label="ans">
<value val="false"/>
<show object="true" label="false" ev="3"/>
<condition showObject="showall ∧ vol"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="894" y="115"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<command name="Segment">
<input a0="A + (l, 0, 0)" a1="A + (l, 0, h)"/>
<output a0="f"/>
</command>
<element type="segment3d" label="f">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="9" y="6"/>
<labelMode val="3"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<caption val="3 cm"/>
</element>
<command name="Segment">
<input a0="A + (l, 0, 0)" a1="A + (l, (-w), 0)"/>
<output a0="g"/>
</command>
<element type="segment3d" label="g">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="15" y="21"/>
<labelMode val="3"/>
<auxiliary val="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<caption val="4 cm"/>
</element>
<command name="Segment">
<input a0="A + (0, (-w), 0)" a1="A + (l, (-w), 0)"/>
<output a0="i"/>
</command>
<element type="segment3d" label="i">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-33" y="25"/>
<labelMode val="3"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<caption val="5 cm"/>
</element>
<command name="Sequence">
<input a0="Sequence[Translate[b, Vector[(i * u1) + (j * u2) + (2 * u3)]], i, 1, l]" a1="j" a2="1" a3="w"/>
<output a0="list2"/>
</command>
<element type="list" label="list2">
<show object="true" label="false" ev="4"/>
<condition showObject="showlayers ∧ (h1 ≥ 2)"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Sequence[Translate[b, Vector[(i * u1) + (j * u2) + (2 * u3)]], i, 1, l]" a1="j" a2="1" a3="w"/>
<output a0="list2'"/>
</command>
<element type="list" label="list2'">
<show object="true" label="false" ev="4"/>
<condition showObject="showlayers ∧ (h1 ≥ 2)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Sequence[Translate[b, Vector[(i * u1) + (j * u2) + (3 * u3)]], i, 1, l]" a1="j" a2="1" a3="w"/>
<output a0="list3"/>
</command>
<element type="list" label="list3">
<show object="true" label="false" ev="4"/>
<condition showObject="showlayers ∧ h1 ≟ 3"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Sequence[Translate[b, Vector[(i * u1) + (j * u2) + (3 * u3)]], i, 1, l]" a1="j" a2="1" a3="w"/>
<output a0="list3'"/>
</command>
<element type="list" label="list3'">
<show object="true" label="false" ev="4"/>
<condition showObject="showlayers ∧ h1 ≟ 3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Translate[b, Vector[(i * u1) + (2 * u2) + u3]]" a1="i" a2="1" a3="l1"/>
<output a0="list12"/>
</command>
<element type="list" label="list12">
<show object="true" label="false" ev="5"/>
<condition showObject="showrows ∧ (w1 ≥ 2)"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Translate[b, Vector[(i * u1) + (2 * u2) + u3]]" a1="i" a2="1" a3="l1"/>
<output a0="list12'"/>
</command>
<element type="list" label="list12'">
<show object="true" label="false" ev="4"/>
<condition showObject="showrows ∧ (w1 ≥ 2)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Translate[b, Vector[(i * u1) + (3 * u2) + u3]]" a1="i" a2="1" a3="l1"/>
<output a0="list13"/>
</command>
<element type="list" label="list13">
<show object="true" label="false" ev="4"/>
<condition showObject="showrows ∧ (w1 ≥ 3)"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Translate[b, Vector[(i * u1) + (3 * u2) + u3]]" a1="i" a2="1" a3="l1"/>
<output a0="list13'"/>
</command>
<element type="list" label="list13'">
<show object="true" label="false" ev="4"/>
<condition showObject="showrows ∧ (w1 ≥ 3)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Translate[b, Vector[(i * u1) + (4 * u2) + u3]]" a1="i" a2="1" a3="l1"/>
<output a0="list14"/>
</command>
<element type="list" label="list14">
<show object="true" label="false" ev="4"/>
<condition showObject="showrows ∧ (w1 ≥ 4)"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Translate[b, Vector[(i * u1) + (4 * u2) + u3]]" a1="i" a2="1" a3="l1"/>
<output a0="list14'"/>
</command>
<element type="list" label="list14'">
<show object="true" label="false" ev="4"/>
<condition showObject="showrows ∧ (w1 ≥ 4)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Translate">
<input a0="b" a1="Vector[u1 + u2 + u3]"/>
<output a0="list01"/>
</command>
<element type="polyhedron" label="list01">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="7"/>
<condition showObject="vol"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Translate">
<input a0="b" a1="Vector[u1 + u2 + u3]"/>
<output a0="list01'"/>
</command>
<element type="polyhedron" label="list01'">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="7"/>
<condition showObject="vol"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Translate">
<input a0="b" a1="Vector[(2 * u1) + u2 + u3]"/>
<output a0="list02"/>
</command>
<element type="polyhedron" label="list02">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="7"/>
<condition showObject="l1 ≥ 2"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Translate">
<input a0="b" a1="Vector[(2 * u1) + u2 + u3]"/>
<output a0="list02'"/>
</command>
<element type="polyhedron" label="list02'">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="7"/>
<condition showObject="l1 ≥ 2"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Translate">
<input a0="b" a1="Vector[(3 * u1) + u2 + u3]"/>
<output a0="list03"/>
</command>
<element type="polyhedron" label="list03">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="7"/>
<condition showObject="l1 ≥ 3"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Translate">
<input a0="b" a1="Vector[(3 * u1) + u2 + u3]"/>
<output a0="list03'"/>
</command>
<element type="polyhedron" label="list03'">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="7"/>
<condition showObject="l1 ≥ 3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Translate">
<input a0="b" a1="Vector[(4 * u1) + u2 + u3]"/>
<output a0="list04"/>
</command>
<element type="polyhedron" label="list04">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="7"/>
<condition showObject="l1 ≥ 4"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Translate">
<input a0="b" a1="Vector[(4 * u1) + u2 + u3]"/>
<output a0="list04'"/>
</command>
<element type="polyhedron" label="list04'">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="7"/>
<condition showObject="l1 ≥ 4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Translate">
<input a0="b" a1="Vector[(5 * u1) + u2 + u3]"/>
<output a0="list05"/>
</command>
<element type="polyhedron" label="list05">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="7"/>
<condition showObject="l1 ≥ 5"/>
<objColor r="255" g="192" b="203" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Translate">
<input a0="b" a1="Vector[(5 * u1) + u2 + u3]"/>
<output a0="list05'"/>
</command>
<element type="polyhedron" label="list05'">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="7"/>
<condition showObject="l1 ≥ 5"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<expression label="textrows" exp=""\;×\;\fgcolor{blue}" + (LaTeX[w1]) + """ />
<element type="text" label="textrows">
<show object="false" label="true" ev="43"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="497" y="114"/>
</element>
<expression label="textlayers" exp=""\;×\;\fgcolor{olivegreen}" + (LaTeX[h1]) + """ />
<element type="text" label="textlayers">
<show object="false" label="false" ev="43"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="482" y="128"/>
</element>
<expression label="total" exp="((l1 * w1) * h1)" />
<element type="numeric" label="total">
<value val="1"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="text2" exp=""\fgcolor{red}" + (LaTeX[l1]) + "\text{ " + (LaTeX[If[l1 > 1, "blocks", "block"]]) + " in each row;}"" />
<element type="text" label="text2">
<show object="true" label="false" ev="11"/>
<condition showObject="vol"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="2" y="73"/>
</element>
<expression label="text3" exp=""\fgcolor{blue}" + (LaTeX[w1]) + "\text{ " + (LaTeX[If[w1 > 1, "rows", "row"]]) + " in each layer;}"" />
<element type="text" label="text3">
<show object="true" label="false" ev="11"/>
<condition showObject="showrows ∧ vol"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="2" y="116"/>
</element>
<expression label="text4" exp=""\fgcolor{olivegreen}" + (LaTeX[h1]) + " \text{ " + (LaTeX[If[h1 > 1, "layers", "layer"]]) + " in total.}"" />
<element type="text" label="text4">
<show object="true" label="false" ev="11"/>
<condition showObject="showlayers ∧ vol"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="1" y="156"/>
</element>
<expression label="text5" exp=""\text{Total number of blocks: }\fgcolor{red}" + (LaTeX[l1]) + "" + (LaTeX[If[showrows, textrows, ""]]) + "" + (LaTeX[If[showlayers, textlayers, ""]]) + "" + (LaTeX[If[showrows, (" = " * total), ""]]) + """ />
<element type="text" label="text5">
<show object="true" label="false" ev="11"/>
<condition showObject="vol"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="337" y="73"/>
</element>
<expression label="text8" exp=""\text{The volume of the cuboid:}\;\;" + (LaTeX[If[ans, text6, ""]]) + """ />
<element type="text" label="text8">
<show object="true" label="false" ev="11"/>
<condition showObject="showall ∧ vol"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="337" y="113"/>
</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="814" y="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="Volume"/>
</element>
<element type="button" label="button7">
<show object="true" label="true" ev="3"/>
<condition showObject="vol"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="534" y="150"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[l1, 1] SetValue[w1, If[l1!=l, 1, w1]] SetValue[h1, If[l1!=l, 1, h1]] SetValue[ans, false] SetValue[vol, false]"/>
<font serif="false" sizeM="2" size="20" style="0"/>
<caption val="Reset"/>
</element>
<expression label="text1" exp=""\text{How many cubic centimetre blocks are required to fill up a cuboid of length} \\\fgcolor{red}" + (LaTeX[l]) + "\text{ cm, width }\fgcolor{blue}" + (LaTeX[w]) + "\text{ cm and height }\fgcolor{OliveGreen}" + (LaTeX[h]) + " \text{ cm? What is the volume of the cuboid?}"" />
<element type="text" label="text1">
<show object="true" label="true" ev="11"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="2" y="3"/>
</element>
</construction>
</geogebra>