<?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 water tank, shaped as a regular prism, is 7/8 full. The diameter of a metal ball equals a quarter of the tank&#39;s height. A number of such balls have been placed into the tank until the water started spilling over. How many balls are there in the tank?</text>
<notepad>
</notepad>
<figures>
<figure>
<name>Watertank</name>
<color>#ffff</color>
<transparent>true</transparent>
<labelled>false</labelled>
<solid>
<points>
<point>
<label>A</label>
<coords>1.0042705098312485 -0.005877852522924771 -0.5</coords>
</point>
<point>
<label>B</label>
<coords>0.3132875042061959 0.9451786637722288 -0.5</coords>
</point>
<point>
<label>C</label>
<coords>-0.8047464845436989 0.5819073997695485 -0.5</coords>
</point>
<point>
<label>F</label>
<coords>1.0042705098312485 -0.005877852522924771 0.5</coords>
</point>
<point>
<label>D</label>
<coords>-0.804746484543699 -0.5936631048153977 -0.5</coords>
</point>
<point>
<label>E</label>
<coords>0.31328750420619567 -0.9569343688180784 -0.5</coords>
</point>
<point>
<label>G</label>
<coords>0.3132875042061959 0.9451786637722288 0.5</coords>
</point>
<point>
<label>H</label>
<coords>-0.8047464845436989 0.5819073997695485 0.5</coords>
</point>
<point>
<label>I</label>
<coords>-0.804746484543699 -0.5936631048153977 0.5</coords>
</point>
<point>
<label>J</label>
<coords>0.31328750420619567 -0.9569343688180784 0.5</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>37.0</value>
</answer>
</problem>
<log>
<action>
<className>GVolumeAction</className>
<figureName>Watertank</figureName>
<variableName>TankVolume</variableName>
</action>
<action>
<className>GMeasureDistanceAction</className>
<figureName>Watertank</figureName>
<p1Label>F</p1Label>
<p2Label>A</p2Label>
<variableName>Height</variableName>
</action>
<action>
<className>GCalcEvaluateAction</className>
<variableName>BallDiameter</variableName>
<expression>Height/4</expression>
</action>
<action>
<className>GCalcEvaluateAction</className>
<variableName>BallVolume</variableName>
<expression>PI*BallDiameter^3/6</expression>
</action>
<action>
<className>GCalcEvaluateAction</className>
<variableName>NumberOfBalls</variableName>
<expression>TankVolume/8/BallVolume</expression>
</action>
<action>
<className>GSolutionAnswerAction</className>
<value>37</value>
</action>
</log>
</solution>