Dynamic Demonstration of Solids of Revolution: Cylinder, Cone, Frustum, Sphere
2020-04-22 11:54
This GeoGebra example dynamically demonstrates the principle of 'a surface moving to form a solid' in solid geometry. Using commands like Surface and Rotate, it visualizes how rotating a rectangle, right triangle, right trapezoid, and semicircle around specific axes generates a cylinder, cone, frustum, and sphere, respectively. It is ideal for high school mathematics education, helping students bu
In collections
立体几何
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.578.0" app="classic" platform="d" id="92b7090f-bf99-4505-9100-ec5918bb555f" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="921" height="725" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.36590662323561346" orientation="1" />
</panes>
<views>
<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="4097" visible="false" inframe="true" stylebar="true" location="1,1" size="395" window="683,364,700,550" />
<view id="1" visible="true" inframe="false" stylebar="true" location="3" size="337" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="280" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<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="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="150" 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 51 | 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="true" location="1" size="563" window="100,100,600,400" />
</views>
<toolbar show="true" items="0 39 73 62 | 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 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6 |" position="1" help="false" />
<input show="true" cmd="true" top="algebra" />
<dockBar show="false" east="true" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="14"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="337" height="526"/>
<coordSystem xZero="148.99999999999997" yZero="263.0" scale="49.99999999999994" yscale="50.0"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<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>
<algebraView>
<mode val="1"/>
</algebraView>
<kernel>
<uses3D val="true"/>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="2" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2.0" max="2.0" step="1.0"/>
<scripting blocked="false" disabled="false"/>
<euclidianView3D>
<coordSystem xZero="0.0" yZero="0.0" zZero="-1.5" scale="60.500000000000014" xAngle="14.0" zAngle="-71.0"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" gridType="3"/>
<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="true"/>
<bgColor r="255" g="255" b="255"/>
<clipping use="false" show="false" size="1"/>
<projection type="0"/>
</euclidianView3D>
<construction title="" author="" date="">
<element type="angle" label="α">
<angleStyle val="3"/>
<value val="0.0"/>
<slider min="0" max="6.283185307179586" absoluteScreenLocation="true" width="180.0" x="19.0" y="49.0" fixed="false" horizontal="true" showAlgebra="true"/>
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="10" type="0" typeHidden="2" opacity="178"/>
<arcSize val="30"/>
<animation step="0.01°" speed="6" type="3" playing="false"/>
</element>
<command name="Surface">
<input a0="cos(θ)" a1="sin(θ)" a2="h" a3="θ" a4="0" a5="α" a6="h" a7="0" a8="3"/>
<output a0="a"/>
</command>
<element type="surfacecartesian3d" label="a">
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 1"/>
<objColor r="0" g="168" b="213" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
</element>
<command name="Polygon">
<input a0="(0, 0, 0)" a1="(1, 0, 0)" a2="(1, 0, 3)" a3="(0, 0, 3)"/>
<output a0="q1" a1="f" a2="g" a3="h" a4="i"/>
</command>
<element type="polygon3d" label="q1">
<lineStyle thickness="0" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 1 ∧ α ≠ 360°"/>
<objColor r="0" g="168" b="213" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment3d" label="f">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="168" b="213" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="g">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="168" b="213" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="h">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="168" b="213" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="i">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="168" b="213" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Rotate">
<input a0="q1" a1="α" a2="zAxis"/>
<output a0="q1'"/>
</command>
<element type="polygon3d" label="q1'">
<lineStyle thickness="0" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 1 ∧ α ≠ 360°"/>
<objColor r="0" g="168" b="213" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Polygon">
<input a0="(0, 0, 0)" a1="(2, 0, 0)" a2="(1, 0, 3)" a3="(0, 0, 3)"/>
<output a0="q2" a1="j" a2="k" a3="l" a4="m"/>
</command>
<element type="polygon3d" label="q2">
<lineStyle thickness="0" type="0" typeHidden="1"/>
<show object="false" label="false" ev="4"/>
<condition showObject="n ≟ 3 ∧ α ≠ 360°"/>
<objColor r="0" g="168" b="213" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment3d" label="j">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="168" b="213" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="k">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="168" b="213" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="l">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="168" b="213" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="m">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="168" b="213" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Rotate">
<input a0="q2" a1="α" a2="zAxis"/>
<output a0="q2'"/>
</command>
<element type="polygon3d" label="q2'">
<lineStyle thickness="0" type="0" typeHidden="1"/>
<show object="false" label="false" ev="4"/>
<condition showObject="n ≟ 3 ∧ α ≠ 360°"/>
<objColor r="0" g="168" b="213" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Surface">
<input a0="((3 - h) / 3 * cos(θ))" a1="((3 - h) / 3 * sin(θ))" a2="h" a3="θ" a4="0" a5="α" a6="h" a7="0" a8="3"/>
<output a0="b"/>
</command>
<element type="surfacecartesian3d" label="b">
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 2"/>
<objColor r="0" g="168" b="213" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
</element>
<command name="Surface">
<input a0="((1.5 * sin(u)) * cos(v))" a1="((1.5 * sin(u)) * sin(v))" a2="(1.5 * cos(u)) + 1.5" a3="u" a4="0" a5="π" a6="v" a7="0" a8="α"/>
<output a0="d"/>
</command>
<element type="surfacecartesian3d" label="d">
<show object="false" label="false" ev="4"/>
<condition showObject="n ≟ 4"/>
<objColor r="0" g="168" b="213" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
</element>
<command name="Surface">
<input a0="((6 - h) / 3 * cos(θ))" a1="((6 - h) / 3 * sin(θ))" a2="h" a3="θ" a4="0" a5="α" a6="h" a7="0" a8="3"/>
<output a0="c"/>
</command>
<element type="surfacecartesian3d" label="c">
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 3"/>
<objColor r="0" g="168" b="213" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
</element>
<element type="numeric" label="n">
<value val="1.0"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelOffset x="0" y="-5"/>
<labelMode val="3"/>
<slider min="1" max="4" absoluteScreenLocation="true" width="200.0" x="52.0" y="106.0" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="3" playing="false"/>
<ggbscript onUpdate="If[n==1,SetCaption[n,"$\Large 矩形$"],n==2,SetCaption[n,"$\Large 直角三角形$"],n==3,SetCaption[n,"$\Large 直角梯形$"],SetCaption[n,"$\Large 半圆$"]]
SetValue[α,0°]"/>
<caption val="$\Large 矩形$"/>
</element>
<element type="button" label="button1">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="81" y="142"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="StartAnimation(α)"/>
<font serif="false" sizeM="2.0" size="14" style="0"/>
<caption val="演示"/>
</element>
<command name="Polygon">
<input a0="(0, 0, 0)" a1="(1, 0, 0)" a2="(0, 0, 3)"/>
<output a0="t1" a1="p" a2="q" a3="r"/>
</command>
<element type="polygon3d" label="t1">
<lineStyle thickness="0" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 2 ∧ α ≠ 360°"/>
<objColor r="0" g="168" b="213" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment3d" label="p">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="168" b="213" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="q">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="168" b="213" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment3d" label="r">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="168" b="213" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Rotate">
<input a0="t1" a1="α" a2="zAxis"/>
<output a0="t1'"/>
</command>
<element type="polygon3d" label="t1'">
<lineStyle thickness="0" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 2 ∧ α ≠ 360°"/>
<objColor r="0" g="168" b="213" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="Line">
<input a0="(0, 0, 0)" a1="(0, 0, 1)"/>
<output a0="s"/>
</command>
<element type="line3d" label="s">
<show object="true" label="false" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="15" typeHidden="1"/>
<coords ox="0.0" oy="0.0" oz="0.0" ow="1.0" vx="0.0" vy="0.0" vz="1.0" vw="0.0"/>
<eqnStyle style="parametric" parameter="λ"/>
</element>
<command name="Semicircle">
<input a0="(0, 0, 0)" a1="(0, 0, 3)" a2="yAxis"/>
<output a0="e"/>
</command>
<element type="conicpart" label="e">
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 4 ∧ α ≠ 360°"/>
<objColor r="0" g="168" b="213" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="0" 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="-2.25" A3="0.0" A4="-0.0" A5="-0.0"/>
<eqnStyle style="parametric"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Rotate">
<input a0="e" a1="α" a2="zAxis"/>
<output a0="e'"/>
</command>
<element type="conicpart" label="e'">
<show object="true" label="false" ev="4"/>
<condition showObject="n ≟ 4 ∧ α ≠ 360°"/>
<objColor r="0" g="168" b="213" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="0" 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="-2.25" A3="0.0" A4="-0.0" A5="-0.0"/>
<eqnStyle style="parametric"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="point" label="A">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0.312" y="-5.252" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="B">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="3.772" y="-5.252" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="image" label="pic1">
<file name="a94857e5933a1326ec9a95938feb52d3/0公众号 二维码.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="A"/>
<startPoint number="1" exp="B"/>
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="text1" exp=""制作教程:""/>
<element type="text" label="text1">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="192" b="203" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="14" style="0"/>
<startPoint x="-2.6400000000000023" y="-0.9400000000000001" z="1.0"/>
</element>
<element type="point" label="C">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-2.748" y="-4.752" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="D">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0.352" y="-4.752" z="1.0"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="image" label="pic2">
<file name="b10eaf757baaa78f81f9b01984f5a669/1587553467.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="C"/>
<startPoint number="1" exp="D"/>
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
</construction>
</geogebra>