Volume of a Rectangular Prism
2016-05-05 14:44
This GeoGebra example demonstrates the volume calculation of a rectangular prism (cuboid) through 3D visualization. Using commands such as Translate, Vector, and Sequence, it constructs an interactive model with adjustable length (l), width (w), and height (h). Interactive buttons allow users to reveal unit cubes row by row, layer by layer, or all at once, helping learners intuitively grasp the ge
<?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="0.5947467166979362" orientation="0" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1,1" size="400" window="593,193,981,666" />
<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="691,127,299,749" />
<view id="16" visible="true" inframe="false" stylebar="false" location="2" size="206" 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="317" 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="206"/>
<coordSystem xZero="179" yZero="315.0000000000003" scale="50" yscale="50.000000000000064"/>
<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="13" zAngle="-69.85047534121243"/>
<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="196" y="87"/>
<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="151" y="87"/>
<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="196" y="127"/>
<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="151" y="127"/>
<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="196" y="167"/>
<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="151" y="167"/>
<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="849" 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="text5" exp=""\text{共有積木： }\fgcolor{red}" + (LaTeX[l1]) + "" + (LaTeX[If[showrows, textrows, ""]]) + "" + (LaTeX[If[showlayers, textlayers, ""]]) + "" + (LaTeX[If[showrows, (" = " * total), ""]]) + "（粒）"" />
<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="317" y="78"/>
</element>
<expression label="text2" exp=""\text{每行 }\fgcolor{red}" + (LaTeX[l1]) + "\text{ 粒；}"" />
<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="78"/>
</element>
<expression label="text3" exp=""\text{每層 }\fgcolor{blue}" + (LaTeX[w1]) + "\text{ 行；}"" />
<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="118"/>
</element>
<expression label="text8" exp=""長方體體積是：\;\;" + (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"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="317" y="118"/>
</element>
<expression label="text4" exp=""\text{共有 }\fgcolor{olivegreen}" + (LaTeX[h1]) + " \text{ 層。}"" />
<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="2" y="158"/>
</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="359" y="35"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="量度體積"/>
</element>
<element type="button" label="button7">
<show object="true" label="true" ev="3"/>
<condition showObject="vol"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="1"/>
<labelOffset x="489" y="160"/>
<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="重設"/>
</element>
<expression label="text1" exp=""\text{要多少粒立方厘米積木，才可填滿一個長 }\fgcolor{red}" + (LaTeX[l]) + "\text{ cm、 闊 }\fgcolor{blue}" + (LaTeX[w]) + "\text{ cm、高 }\fgcolor{OliveGreen}" + (LaTeX[h]) + " \text{ cm 的長方體？} \\\text{長方體的體積是多少？}"" />
<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"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="2" y="3"/>
</element>
</construction>
</geogebra>