<?xml version="1.0" encoding="UTF-8"?>
<solution xmlns="http://geocentral.net">
<version>3.1</version>
<envelope>
<author>
<name>Stelian Dumitrascu</name>
<email>stelian@geocentral.net</email>
<web>http://geocentral.net/geometria</web>
</author>
<comments>This is the solution of a sample Geometria problem.</comments>
</envelope>
<problem>
<envelope>
<author>
<name>Stelian Dumitrascu</name>
<email>stelian@geocentral.net</email>
<web>http://geocentral.net/geometria</web>
</author>
<comments>This is a sample Geometria problem.</comments>
</envelope>
<text>This cube is to be carved into a cylinder whose radius is six times shorter than the cube&#39;s side. What is the maximum volume of the cylinder.</text>
<notepad>
</notepad>
<figures>
<figure>
<name>Cube</name>
<color>#ff9999</color>
<transparent>false</transparent>
<labelled>true</labelled>
<solid>
<points>
<point>
<label>A</label>
<coords>-1.0 -1.0 -1.0</coords>
</point>
<point>
<label>B</label>
<coords>1.0 -1.0 -1.0</coords>
</point>
<point>
<label>C</label>
<coords>1.0 1.0 -1.0</coords>
</point>
<point>
<label>E</label>
<coords>-1.0 -1.0 1.0</coords>
</point>
<point>
<label>D</label>
<coords>-1.0 1.0 -1.0</coords>
</point>
<point>
<label>F</label>
<coords>1.0 -1.0 1.0</coords>
</point>
<point>
<label>G</label>
<coords>1.0 1.0 1.0</coords>
</point>
<point>
<label>H</label>
<coords>-1.0 1.0 1.0</coords>
</point>
</points>
<lines>
</lines>
</solid>
<camera>
<attitude>-0.5328608041697043 -0.3348186344436886 -0.41346657962945993 0.6580282918981487</attitude>
</camera>
</figure>
</figures>
<answer>
<type>number</type>
<value>0.8800971362925621</value>
</answer>
</problem>
<log>
<action>
<className>GCutAction</className>
<figureName>Cube</figureName>
<p0Label>A</p0Label>
<p1Label>E</p1Label>
<p2Label>G</p2Label>
<figure1Name>Figure1</figure1Name>
<figure2Name>Figure2</figure2Name>
</action>
<action>
<className>GDrawLineAction</className>
<figureName>Figure2</figureName>
<p1Label>A</p1Label>
<p2Label>G</p2Label>
</action>
<action>
<className>GMeasureDistanceAction</className>
<figureName>Figure2</figureName>
<p1Label>A</p1Label>
<p2Label>E</p2Label>
<variableName>Side</variableName>
</action>
<action>
<className>GCalcEvaluateAction</className>
<variableName>Radius</variableName>
<expression>Side/6</expression>
</action>
<action>
<className>GMeasureAngleAction</className>
<figureName>Figure2</figureName>
<p0Label>G</p0Label>
<p1Label>E</p1Label>
<p2Label>A</p2Label>
<variableName>Angle</variableName>
</action>
<action>
<className>GLayDistanceAction</className>
<figureName>Figure2</figureName>
<distance>Radius/sin(Angle)</distance>
<p0Label>G</p0Label>
<p1Label>E</p1Label>
<p2Label>G</p2Label>
</action>
<action>
<className>GPerpendicularAction</className>
<figureName>Figure2</figureName>
<p0Label>I</p0Label>
<p1Label>A</p1Label>
<p2Label>G</p2Label>
</action>
<action>
<className>GLayDistanceAction</className>
<figureName>Figure2</figureName>
<distance>Radius/sin(Angle)</distance>
<p0Label>A</p0Label>
<p1Label>C</p1Label>
<p2Label>A</p2Label>
</action>
<action>
<className>GPerpendicularAction</className>
<figureName>Figure2</figureName>
<p0Label>K</p0Label>
<p1Label>A</p1Label>
<p2Label>G</p2Label>
</action>
<action>
<className>GIntersectAction</className>
<figureName>Figure2</figureName>
<p11Label>K</p11Label>
<p12Label>L</p12Label>
<p21Label>A</p21Label>
<p22Label>G</p22Label>
</action>
<action>
<className>GIntersectAction</className>
<figureName>Figure2</figureName>
<p11Label>I</p11Label>
<p12Label>J</p12Label>
<p21Label>A</p21Label>
<p22Label>G</p22Label>
</action>
<action>
<className>GMeasureDistanceAction</className>
<figureName>Figure2</figureName>
<p1Label>M</p1Label>
<p2Label>N</p2Label>
<variableName>Height</variableName>
</action>
<action>
<className>GCalcEvaluateAction</className>
<variableName>Ratio</variableName>
<expression>Height/Side</expression>
</action>
<action>
<className>GSolutionAnswerAction</className>
<value>pi * Radius^2 * Height</value>
</action>
</log>
</solution>