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<Input><Text-field style="Title" layout="Title">Bodies with fixed volume and minimal surface</Text-field><Text-field style="Author" size="11" layout="Author"><Font size="11">Author: Valery Ochkov (http://twt.mpei.ac.ru/ochkov/v_ochkov.htm)</Font></Text-field><Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart</Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="h__1 := solve(V = (1/4)*Pi*d^2*h, h)" display="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">PkklaF9fMUc2Ii1JJnNvbHZlR0YkNiQvSSJWR0YkLCQqKEkjUGlHJSpwcm90ZWN0ZWRHIiIiSSJkR0YkIiIjSSJoR0YkRi4jRi4iIiVGMQ==</Equation></Text-field>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKEkiVkc2IiIiIkkjUGlHJSpwcm90ZWN0ZWRHISIiSSJkR0YlISIjIiIl</Equation></Text-field>
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<Group labelreference="L669" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Surface (S as function of V and d)</Text-field>
</Input>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="S := subs(h = h__1, (1/4)*Pi*d^2+Pi*d*h)" display="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">PkkiU0c2Ii1JJXN1YnNHJSpwcm90ZWN0ZWRHNiQvSSJoR0YkSSVoX18xR0YkLCYqJkkjUGlHRiciIiJJImRHRiQiIiMjRi8iIiUqKEYuRi9GMEYvRipGL0Yv</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqJkkjUGlHJSpwcm90ZWN0ZWRHIiIiSSJkRzYiIiIjI0YmIiIlKiZGJyEiIkkiVkdGKEYmRis=</Equation></Text-field>
</Output>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="d__optimal := solve(diff(S, d), d)" display="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">PkkrZF9fb3B0aW1hbEc2Ii1JJnNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiQtSSVkaWZmR0YoNiRJIlNHRiRJImRHRiRGLw==</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NiUsJComSSNQaUclKnByb3RlY3RlZEchIiIqJkkiVkc2IiIiIkYlIiIjI0YrIiIkRiwsJkYkRicqKl4jRitGK0YuI0YrRixGJUYnRihGLUYrLCZGJEYnKipeI0YnRitGLkYyRiVGJ0YoRi1GKw==</Equation></Text-field>
</Output>
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<Input><Text-field style="Text" layout="Normal">A = d / h if S is minimal</Text-field>
</Input>
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<Group hide-input="false" hide-output="false" labelreference="L672" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="A := simplify(d__optimal/(eval(h__1, d = d__optimal)))" display="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">PkkiQUc2Ii1JKXNpbXBsaWZ5RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqJkkrZF9fb3B0aW1hbEdGJCIiIi1JJWV2YWxHRig2JEklaF9fMUdGJC9JImRHRiRGLCEiIg==</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKn4mIzg3ODg7fkYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZMLUkjbW5HRiQ2JFEiMkYnRjkvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRj1GOQ==">IiIj</Equation></Text-field>
</Output>
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</Section>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" layout="Heading 1">2. Cylinder with a bottom (see above) and a cover</Text-field></Title>
<Group hide-input="false" hide-output="false" labelreference="L836" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="h__1 := solve(V = (1/4)*Pi*d^2*h, h)" display="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">PkklaF9fMUc2Ii1JJnNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiQvSSJWR0YkLCQqKEkjUGlHRigiIiJJImRHRiQiIiNJImhHRiRGMCNGMCIiJUYz</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKEkiVkc2IiIiIkkjUGlHJSpwcm90ZWN0ZWRHISIiSSJkR0YlISIjIiIl</Equation></Text-field>
</Output>
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<Group labelreference="L843" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal">Surface (S as function of V and d)</Text-field>
</Input>
</Group>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="S := subs(h = h__1, (1/4)*Pi*d^2+Pi*d*h+(1/4)*Pi*d^2)" display="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">PkkiU0c2Ii1JJXN1YnNHJSpwcm90ZWN0ZWRHNiQvSSJoR0YkSSVoX18xR0YkLUkiK0dGJzYkLCYqJkkjUGlHRiciIiJJImRHRiQiIiMjRjIiIiUqKEYxRjJGM0YyRipGMkYyLCRGMEY1</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqJkkjUGlHJSpwcm90ZWN0ZWRHIiIiSSJkRzYiIiIjI0YmRikqJkYnISIiSSJWR0YoRiYiIiU=</Equation></Text-field>
</Output>
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<Group hide-input="false" hide-output="false" labelreference="L842" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="d__optimal := solve(diff(S, d), d)" display="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">PkkrZF9fb3B0aW1hbEc2Ii1JJnNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiQtSSVkaWZmR0YoNiRJIlNHRiRJImRHRiRGLw==</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NiUqKEkjUGlHJSpwcm90ZWN0ZWRHISIiIiIlIyIiIiIiJComSSJWRzYiRilGJCIiI0YoLCZGIyNGJkYuKixeIyNGKUYuRilGKkYzRiRGJkYnRihGK0YoRiksJkYjRjAqLF4jRjBGKUYqRjNGJEYmRidGKEYrRihGKQ==</Equation></Text-field>
</Output>
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<Input><Text-field style="Text" layout="Normal">A = d / h if S is minimal</Text-field>
</Input>
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<Group hide-input="false" hide-output="false" labelreference="L837" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="A := simplify(d__optimal/(eval(h__1, d = d__optimal)))" display="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">PkkiQUc2Ii1JKXNpbXBsaWZ5RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqJkkrZF9fb3B0aW1hbEdGJCIiIi1JJWV2YWxHRig2JEklaF9fMUdGJC9JImRHRiRGLCEiIg==</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKn4mIzg3ODg7fkYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZMLUkjbW5HRiQ2JFEiMUYnRjkvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRj1GOQ==">IiIi</Equation></Text-field>
</Output>
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</Section>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" layout="Heading 1">3. Cylinder with a bottom and one central vertical dividing wall</Text-field></Title>
<Group hide-input="false" hide-output="false" labelreference="L725" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="h__1 := solve(V = (1/4)*Pi*d^2*h, h)" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2KC1GLDYjUSdgaF9fMWBGJy1JI21vR0YkNi5RKiZjb2xvbmVxO0YnLyUnZmFtaWx5R1EmQXJpYWxGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkAvJSlzdHJldGNoeUdGQC8lKnN5bW1ldHJpY0dGQC8lKGxhcmdlb3BHRkAvJS5tb3ZhYmxlbGltaXRzR0ZALyUnYWNjZW50R0ZALyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTy1GNTYuUSJ+RidGOEY7Rj5GQUZDRkVGR0ZJRksvRk5RJjAuMGVtRicvRlFGVi1GLDYmUSZzb2x2ZUYnRjgvJSdpdGFsaWNHUSV0cnVlRicvRjxRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNi4tRiw2JlEiVkYnRjgvRmZuRkBGOy1GNTYuUSI9RidGOEY7Rj5GQUZDRkVGR0ZJRktGTUZQRlItRiw2JlElJnBpO0YnRjhGYm9GOy1GNTYuUScmc2RvdDtGJ0Y4RjtGPkZBRkNGRUZHRklGS0ZVRlctSSZtZnJhY0dGJDYoLUYjNiQtSSVtc3VwR0YkNiUtRiw2JlEiZEYnRjhGYm9GOy1GIzYkLUkjbW5HRiQ2JVEiMkYnRjhGO0Y7LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Y7LUYjNiQtRmpwNiVRIjRGJ0Y4RjtGOy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGanEvJSliZXZlbGxlZEdGQEZpby1GLDYmUSJoRidGOEZlbkZobi1GNTYtUSIsRidGO0Y+L0ZCRmduRkNGRUZHRklGS0ZVL0ZRUSwwLjMzMzMzMzNlbUYnLUY1Ni1GVEY7Rj5GQUZDRkVGR0ZJRktGVUZXLUYsNiVGYXJGZW5GaG5GO0Y4RjtGO0YrLyUrZXhlY3V0YWJsZUdGQEY7">PkklaF9fMUc2Ii1JJnNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiQvSSJWR0YkLCQqKEkjUGlHRigiIiJJImRHRiQiIiNJImhHRiRGMCNGMCIiJUYz</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKEkiVkc2IiIiIkkjUGlHJSpwcm90ZWN0ZWRHISIiSSJkR0YlISIjIiIl</Equation></Text-field>
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<Group hide-input="false" hide-output="false" labelreference="L726" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="S := subs(h = h__1, (1/4)*Pi*d^2+Pi*d*h+d*h)" display="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">PkkiU0c2Ii1JJXN1YnNHJSpwcm90ZWN0ZWRHNiQvSSJoR0YkSSVoX18xR0YkLCgqJkkjUGlHRiciIiJJImRHRiQiIiMjRi8iIiUqKEYuRi9GMEYvRipGL0YvKiZGMEYvRipGL0Yv</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqJkkjUGlHJSpwcm90ZWN0ZWRHIiIiSSJkRzYiIiIjI0YmIiIlKiZGJyEiIkkiVkdGKEYmRisqKEYnRi1GLkYmRiRGLUYr</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="d__optimal := solve(diff(S, d), d)" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EtYGRfX29wdGltYWxgRictSSNtb0dGJDYtUSomY29sb25lcTtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRy1GLDYlUSZzb2x2ZUYnLyUnaXRhbGljR1EldHJ1ZUYnL0Y0USdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYpLUkmbWZyYWNHRiQ2KC1GMDYtUTAmRGlmZmVyZW50aWFsRDtGJ0YzL0Y3USZ1bnNldEYnL0Y6RmhuL0Y8RmhuL0Y+RmhuL0ZARmhuL0ZCRmhuL0ZERmhuL0ZGUSYwLjBlbUYnL0ZJRmBvLUYjNiZGWi1GMDYtUSJ+RidGM0Y2RjlGO0Y9Rj9GQUZDRl9vRmFvLUYsNiVRImRGJ0ZNRlBGMy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGX3AvJSliZXZlbGxlZEdGOEZkby1GLDYlUSJTRidGTUZQLUYwNi1RIixGJ0YzRjYvRjpGT0Y7Rj1GP0ZBRkNGX28vRklRLDAuMzMzMzMzM2VtRidGZ28vJStleGVjdXRhYmxlR0Y4RjNGM0ZdcUYz">PkkrZF9fb3B0aW1hbEc2Ii1JJnNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiQtSSVkaWZmR0YoNiRJIlNHRiRJImRHRiRGLw==</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NiUsJComSSNQaUclKnByb3RlY3RlZEchIiIqKEkiVkc2IiIiIiwmRiVGK0YrRitGK0YlRisjRisiIiQiIiMsJkYkRicqKl4jRitGK0YuI0YrRi9GJUYnRihGLUYrLCZGJEYnKipeI0YnRitGLkYzRiVGJ0YoRi1GKw==</Equation></Text-field>
</Output>
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<Group hide-input="false" hide-output="false" labelreference="L724" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="A := simplify(d__optimal/(eval(h__1, d = d__optimal)))" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRKXNpbXBsaWZ5RidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiUtSSZtZnJhY0dGJDYoLUYjNigtRiw2I1EtYGRfX29wdGltYWxgRicvJStmb3JlZ3JvdW5kR1EqWzAsMCwyNTVdRicvJStleGVjdXRhYmxlR0Y9LyUpcmVhZG9ubHlHRjEvJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGJ0Y5LUYjNictRiw2I1EhRictRiM2J0Zlby1GWDYoLUYjNictRiw2I1EnYGhfXzFgRidGZW8vJSxwbGFjZWhvbGRlckdGMS8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGMUY5LUkpbXBoYW50b21HRiQ2JC1GIzYmRmVvLUYjNiZGZW8tRiM2J0Zlby1GLDYlUSJ4RidGL0YyLUY2Ni1RIj1GJ0Y5L0Y8USZ1bnNldEYnL0Y/RmVxL0ZBRmVxL0ZDRmVxL0ZFRmVxL0ZHRmVxL0ZJRmVxRkpGTS1GLDYlUSJhRidGL0YyRjlGZW9GOUZlb0Y5LyUsY29uc3RyYWludHNHUSxoZWlnaHQtb25seUYnLyUubGluZXRoaWNrbmVzc0dRIjBGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Znci8lKWJldmVsbGVkR0Y9LUY2Ni1RKSZ2ZXJiYXI7RidGOUZkcUZmcS9GQUYxRmhxRmlxRmpxRltyL0ZLUSwwLjExMTExMTFlbUYnL0ZORmFzLUZYNigtRmZwNiQtRiM2JkZlby1GIzYlRmVvLUYsNiVRJWYoeClGJ0YvRjJGOUZlb0Y5Rl9yLUYjNiYtRiw2JVEiZEYnRi9GMi1GNjYtRmNxRjlGO0Y+RkBGQkZERkZGSEZKRk1GZm5GOUZickZlckZockZqckY5RmVvRi9GMi9GY3JRIjFGJ0ZlckZockZqckZcb0Y5RjlGXG9GOQ==">PkkiQUc2Ii1JKXNpbXBsaWZ5RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqJkkrZF9fb3B0aW1hbEdGJCIiIi1JJWV2YWxHRig2JEklaF9fMUdGJC9JImRHRiRGLCEiIg==</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYsJkkjUGlHJSpwcm90ZWN0ZWRHIiIjRiYiIiJGJ0YkISIi</Equation></Text-field>
</Output>
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<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKEkiVkc2IiIiIkkjUGlHJSpwcm90ZWN0ZWRHISIiSSJkR0YlISIjIiM3</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="S := subs(h = h__1, (1/2)*Pi*d*sqrt((1/4)*d^2+h^2))" display="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">PkkiU0c2Ii1JJXN1YnNHJSpwcm90ZWN0ZWRHNiQvSSJoR0YkSSVoX18xR0YkLCQqKEkjUGlHRiciIiJJImRHRiRGLy1JJXNxcnRHNiRGJ0koX3N5c2xpYkdGJDYjLCYqJEYwIiIjI0YvIiIlKiRGKkY4Ri9GLyNGL0Y4</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKn4mIzg3ODg7fkYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZMLUYjNigtSSZtZnJhY0dGJDYoLUkjbW5HRiQ2JFEiMUYnRjktRlU2JFEiNEYnRjkvJS5saW5ldGhpY2tuZXNzR0ZXLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmluLyUpYmV2ZWxsZWRHRj0tRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSEZKRk0tRiM2KC1GLDYlUScmIzk2MDtGJy9GMEY9RjlGXm8tRiw2JVEiZEYnRi9GMkZeby1JJm1zcXJ0R0YkNiMtRiM2Ji1GIzYkLUklbXN1cEdGJDYlRmdvLUZVNiRRIjJGJ0Y5LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Y5LUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GXnEtRlI2KC1GIzYoLUZVNiRRJDU3NkYnRjlGXm8tRmJwNiUtRiw2JVEiVkYnRi9GMkZkcEZncC8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGPUY5LUYjNigtRmJwNiVGY29GZHBGZ3BGXm8tRmJwNiVGZ29GWEZncEZcckZfckY5RmVuRmduRmpuRlxvRjlGOUZcckZfckY5RlxyRl9yRjk=">LCQqKEkjUGlHJSpwcm90ZWN0ZWRHIiIiSSJkRzYiRiYsJiokRiciIiNGJiooSSJWR0YoRitGJCEiI0YnISIlIiR3JiNGJkYrI0YmIiIl</Equation></Text-field>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="d__optimal := solve(diff(S, d), d)" display="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">PkkrZF9fb3B0aW1hbEc2Ii1JJnNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiQtSSVkaWZmR0YoNiRJIlNHRiRJImRHRiRGLw==</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NigqKCIkKUcjIiIiIiInSSNQaUclKnByb3RlY3RlZEchIiIqJkkiVkc2IiIiI0YoIiIlRiUqKiwmI0YmRi5GJiomXiNGMkYmIiIkRjJGJkYmRiRGJUYoRipGK0YlKiosJiNGKkYuRiZGM0YmRiZGJEYlRihGKkYrRiUsJEYjRioqKiwmRjhGJiomXiNGOEYmRjVGMkYmRiZGJEYlRihGKkYrRiUqKiwmRjJGJkY8RiZGJkYkRiVGKEYqRitGJQ==</Equation></Text-field>
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<Group hide-input="false" hide-output="false" labelreference="L504" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="A := simplify(d__optimal/(eval(h__1, d = d__optimal)))" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRKXNpbXBsaWZ5RidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiUtSSZtZnJhY0dGJDYoLUYjNigtRiw2I1EtYGRfX29wdGltYWxgRicvJStmb3JlZ3JvdW5kR1EqWzAsMCwyNTVdRicvJStleGVjdXRhYmxlR0Y9LyUpcmVhZG9ubHlHRjEvJTBmb250X3N0eWxlX25hbWVHUSoyRH5PdXRwdXRGJ0Y5LUYjNictRiw2I1EhRictRiM2J0Zlby1GWDYoLUYjNictRiw2I1EnYGhfXzFgRidGZW8vJSxwbGFjZWhvbGRlckdGMS8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdGMUY5LUkpbXBoYW50b21HRiQ2JC1GIzYmRmVvLUYjNiZGZW8tRiM2J0Zlby1GLDYlUSJ4RidGL0YyLUY2Ni1RIj1GJ0Y5L0Y8USZ1bnNldEYnL0Y/RmVxL0ZBRmVxL0ZDRmVxL0ZFRmVxL0ZHRmVxL0ZJRmVxRkpGTS1GLDYlUSJhRidGL0YyRjlGZW9GOUZlb0Y5LyUsY29uc3RyYWludHNHUSxoZWlnaHQtb25seUYnLyUubGluZXRoaWNrbmVzc0dRIjBGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Znci8lKWJldmVsbGVkR0Y9LUY2Ni1RKSZ2ZXJiYXI7RidGOUZkcUZmcS9GQUYxRmhxRmlxRmpxRltyL0ZLUSwwLjExMTExMTFlbUYnL0ZORmFzLUZYNigtRmZwNiQtRiM2JkZlby1GIzYlRmVvLUYsNiVRJWYoeClGJ0YvRjJGOUZlb0Y5Rl9yLUYjNiYtRiw2JVEiZEYnRi9GMi1GNjYtRmNxRjlGO0Y+RkBGQkZERkZGSEZKRk1GZm5GOUZickZlckZockZqckY5RmVvRi9GMi9GY3JRIjFGJ0ZlckZockZqckZcb0Y5RjlGXG9GOQ==">PkkiQUc2Ii1JKXNpbXBsaWZ5RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqJkkrZF9fb3B0aW1hbEdGJCIiIi1JJWV2YWxHRig2JEklaF9fMUdGJC9JImRHRiRGLCEiIg==</Equation></Text-field>
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<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" layout="Heading 1">5. Cone with base (a wineglass)</Text-field></Title>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="S := subs(h = h__1, (1/2)*Pi*d*sqrt(((1/2)*d)^2+h^2)+(1/4)*Pi*d^2)" display="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">PkkiU0c2Ii1JJXN1YnNHJSpwcm90ZWN0ZWRHNiQvSSJoR0YkSSVoX18xR0YkLCYqKEkjUGlHRiciIiJJImRHRiRGLy1JJXNxcnRHNiRGJ0koX3N5c2xpYkdGJDYjLCYtSSJeR0YnNiQsJEYwI0YvIiIjRjxGLyokRipGPEYvRi9GOyomRi5GL0YwRjwjRi8iIiU=</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqKEkjUGlHJSpwcm90ZWN0ZWRHIiIiSSJkRzYiRiYsJiokRiciIiNGJiooSSJWR0YoRitGJCEiI0YnISIlIiR3JiNGJkYrI0YmIiIlKiZGJEYmRidGK0Yy</Equation></Text-field>
</Output>
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<Group hide-input="false" hide-output="false" labelreference="L688" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="d__optimal := solve(diff(S, d), d)" display="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">PkkrZF9fb3B0aW1hbEc2Ii1JJnNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiQtSSVkaWZmR0YoNiRJIlNHRiRJImRHRiRGLw==</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NigqKCIjcyMiIiIiIidJI1BpRyUqcHJvdGVjdGVkRyEiIiomSSJWRzYiIiIjRigiIiVGJSoqLCYjRiZGLkYmKiZeI0YyRiYiIiRGMkYmRiZGJEYlRihGKkYrRiUqKiwmI0YqRi5GJkYzRiZGJkYkRiVGKEYqRitGJSwkRiNGKioqLCZGOEYmKiZeI0Y4RiZGNUYyRiZGJkYkRiVGKEYqRitGJSoqLCZGMkYmRjxGJkYmRiRGJUYoRipGK0Yl</Equation></Text-field>
</Output>
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<Group hide-input="false" hide-output="false" labelreference="L696" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="A := simplify(d__optimal/(eval(h__1, d = d__optimal)))" display="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">PkkiQUc2Ii1JKXNpbXBsaWZ5RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqJkkrZF9fb3B0aW1hbEdGJCIiIi1JJWV2YWxHRig2JEklaF9fMUdGJC9JImRHRiRGLCEiIg==</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJiIiIyMiIiJGJC1JJWNzZ25HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kiVkdGLEYmRiU=</Equation></Text-field>
</Output>
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<Group hide-input="false" hide-output="false" labelreference="L710" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="evalf(A)" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSZldmFsZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRIkFGJ0Y0RjcvRjhRJ25vcm1hbEYnRkJGQkYrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGQg==">LUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiNJIkFHNiI=</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQtSSVjc2duRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJIlZHRigkIis1eTFycSEjNQ==</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" layout="Heading 1">6. Cone with base (see above) and cover (a cap)</Text-field></Title>
<Group hide-input="false" hide-output="false" labelreference="L705" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="h__1 := solve(V = ((1/3)*Pi*((1/4)*d^2))*h, h)" display="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">PkklaF9fMUc2Ii1JJnNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiQvSSJWR0YkKiYtSSIqR0YoNiQsJEkjUGlHRigjIiIiIiIkLCQqJEkiZEdGJCIiIyNGNCIiJUY0SSJoR0YkRjRGPA==</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKEkiVkc2IiIiIkkjUGlHJSpwcm90ZWN0ZWRHISIiSSJkR0YlISIjIiM3</Equation></Text-field>
</Output>
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<Group hide-input="false" hide-output="false" labelreference="L701" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="S := subs(h = h__1, (1/2)*Pi*d*sqrt(((1/2)*d)^2+h^2)+(1/4)*Pi*d^2+(1/4)*Pi*d^2)" display="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">PkkiU0c2Ii1JJXN1YnNHJSpwcm90ZWN0ZWRHNiQvSSJoR0YkSSVoX18xR0YkLUkiK0dGJzYkLCYqKEkjUGlHRiciIiJJImRHRiRGMi1JJXNxcnRHNiRGJ0koX3N5c2xpYkdGJDYjLCYtSSJeR0YnNiQsJEYzI0YyIiIjRj9GMiokRipGP0YyRjJGPiomRjFGMkYzRj8jRjIiIiUsJEZBRkI=</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqKEkjUGlHJSpwcm90ZWN0ZWRHIiIiSSJkRzYiRiYsJiokRiciIiNGJiooSSJWR0YoRitGJCEiI0YnISIlIiR3JiNGJkYrI0YmIiIlKiZGJEYmRidGK0Yx</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" hide-output="false" labelreference="L699" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="d__optimal := solve(diff(S, d), d)" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EtYGRfX29wdGltYWxgRictSSNtb0dGJDYtUSomY29sb25lcTtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRy1GLDYlUSZzb2x2ZUYnLyUnaXRhbGljR1EldHJ1ZUYnL0Y0USdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYpLUkmbWZyYWNHRiQ2KC1GMDYtUTAmRGlmZmVyZW50aWFsRDtGJ0YzL0Y3USZ1bnNldEYnL0Y6RmhuL0Y8RmhuL0Y+RmhuL0ZARmhuL0ZCRmhuL0ZERmhuL0ZGUSYwLjBlbUYnL0ZJRmBvLUYjNiZGWi1GMDYtUSJ+RidGM0Y2RjlGO0Y9Rj9GQUZDRl9vRmFvLUYsNiVRImRGJ0ZNRlBGMy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGX3AvJSliZXZlbGxlZEdGOEZkby1GLDYlUSJTRidGTUZQLUYwNi1RIixGJ0YzRjYvRjpGT0Y7Rj1GP0ZBRkNGX28vRklRLDAuMzMzMzMzM2VtRidGZ28vJStleGVjdXRhYmxlR0Y4RjNGM0ZdcUYz">PkkrZF9fb3B0aW1hbEc2Ii1JJnNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiQtSSVkaWZmR0YoNiRJIlNHRiRJImRHRiRGLw==</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ni4qKCIjJyojIiIiIiInSSNQaUclKnByb3RlY3RlZEchIiIqKEYoIiIlSSJWRzYiIiIjLCYqJCIiKCNGJkYvRi8hIiZGJkYmRiUqKiwmRjNGJiomXiNGM0YmIiIkRjNGJkYmRiRGJUYoRipGK0YlKiosJiNGKkYvRiZGN0YmRiZGJEYlRihGKkYrRiUsJEYjRioqKiwmRjxGJiomXiNGPEYmRjlGM0YmRiZGJEYlRihGKkYrRiUqKiwmRjNGJkZARiZGJkYkRiVGKEYqRitGJSooRiRGJUYoRiosJCooRihGLEYtRi8sJkYxRi8iIiZGJkYmRipGJSoqRjZGJkYkRiVGKEYqRkVGJSoqRjtGJkYkRiVGKEYqRkVGJSwkRkRGKioqRj9GJkYkRiVGKEYqRkVGJSoqRkNGJkYkRiVGKEYqRkVGJQ==</Equation></Text-field>
</Output>
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<Section collapsed="false" isCollapsible="true" drawButton="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Text-field style="Heading 1" layout="Heading 1">7. Cone with semisphere - Can you get the solution? And for others bodies!</Text-field></Title>
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</Input>
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<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="d__optimal := allvalues(d__optimal)" display="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">PkkrZF9fb3B0aW1hbEc2Ii1JKmFsbHZhbHVlc0dGJDYjRiM=</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkqbWNvbXBsZXRlR0YkNiQtSSNtaUdGJDYjUS1gZF9fb3B0aW1hbGBGJy1GLzYlUStkX19vcHRpbWFsRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqfiYjODc4ODt+RicvRjlRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZDLyUpc3RyZXRjaHlHRkMvJSpzeW1tZXRyaWNHRkMvJShsYXJnZW9wR0ZDLyUubW92YWJsZWxpbWl0c0dGQy8lJ2FjY2VudEdGQy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlItRiM2PC1GIzYoLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJ0Y/LUZnbjYkUSI1RidGPy8lLmxpbmV0aGlja25lc3NHRmluLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmFvLyUpYmV2ZWxsZWRHRkMtRjw2LVExJkludmlzaWJsZVRpbWVzO0YnRj9GQUZERkZGSEZKRkxGTkZQRlMtRlo2KC1GIzYoLUklbXN1cEdGJDYlLUZnbjYkUSQxMDBGJ0Y/LUYjNihGZm4tRjw2LVEiL0YnRj9GQUZEL0ZHRjdGSEZKRkxGTi9GUVEsMC4xNjY2NjY3ZW1GJy9GVEZqcC1GZ242JFEiM0YnRj8vJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUpcmVhZG9ubHlHRkNGPy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGZm8tRl5wNiUtSShtZmVuY2VkR0YkNiQtRiM2KC1GLzYlUSJWRidGNUY4RmZvLUZqcTYkLUYjNigtRiM2Ji1JJm1zcXJ0R0YkNiNGXHFGZm8tRmhyNiMtRlo2KC1GIzYmLUYjNigtRiM2JkZqbkZmby1GXnA2JS1GanE2JC1GIzYmLUYjNiYtRiM2Ji1GZ242JFEjMThGJ0Y/RmZvLUZnbjYkUSJJRidGP0Y/RmZvLUZocjYjLUZnbjYkUSQ1MDNGJ0Y/Rj8tRjw2LVEiK0YnRj9GQUZERkZGSEZKRkxGTi9GUVEsMC4yMjIyMjIyZW1GJy9GVEZddS1GZ242JFEkMjUzRidGP0Y/Rj8tRiM2KC1GZ242JFEiMkYnRj9GZXBGXHFGX3FGYnFGP0ZkcUY/Rml0LUYjNiYtRmduNiRRJDEwN0YnRj9GZm8tRl5wNiVGZnNGY3BGZHFGP0ZpdC1GZ242JFEkMzA1RidGP0Y/Rl9xRmJxRj8tRiM2JkZcdkZfcUZicUY/Rl1vRl9vRmJvRmRvRj9GaXQtRiM2JC1GaHI2Iy1GIzYnLUY8Ni1RKiZ1bWludXMwO0YnRj9GQUZERkZGSEZKRkxGTkZcdUZedS1GWjYoLUYjNihGXHFGZm8tRmpxNiQtRiM2Ki1GIzYoRmpuRmZvRmpyRmZvRmRzRj9GaXQtRiM2KC1GZ242JFElMTAzMkYnRj9GZm9GZ3JGZm9GXHZGPy1GPDYtUSgmbWludXM7RidGP0ZBRkRGRkZIRkpGTEZORlx1Rl51LUYjNigtRmduNiRRJDIxNEYnRj9GZm9GXHZGZm9GanJGP0ZpdC1GIzYmRl52RmZvRmpyRj9GP0Y/Rl9xRmJxRj8tRiM2KEZcdkZmb0ZqckZfcUZicUY/Rl1vRl9vRmJvRmRvRl9xRmJxRj9GP0ZbeC1GZ242JFEiOUYnRj9GP0Y/RmZvLUZecDYlLUYvNiVRJyYjOTYwO0YnL0Y2RkNGP0ZkdUZkcUY/Rj9GY3BGZHFGX3FGYnFGPy1GIzYmRlx5Rl9xRmJxRj9GXW9GX29GYm9GZG9GX3FGYnFGPy1GPDYtUSIsRidGP0ZBL0ZFRjdGRkZIRkpGTEZORlAvRlRRLDAuMzMzMzMzM2VtRictRiM2J0Zpdi1GIzYoLUZaNihGZm4tRmduNiRRIzEwRidGP0Zdb0Zfb0Zib0Zkb0Zmb0Zpb0ZfcUZicUY/Rml0LUZaNigtRiM2LC1GIzYoRlx6RmZvLUYjNiRGYXRGP0ZfcUZicUY/RmZvRmdyRmZvRl1wRmZvRmdxRl9xRmJxRj9GYHlGXW9GX29GYm9GZG9GP0ZieS1GIzYnRml2Rmp5Rlt4RmF6Rj9GYnktRiM2KEZZRmZvLUZaNigtRiM2Ji1GXnA2JS1GanE2JC1GIzYnRml2LUYjNipGYHBGZm9GXnJGZm8tRmpxNiQtRiM2KUZpdkZlckZpdEZjdkZpdEZneEY/Rj9GZm9GanhGP0ZfcUZicUY/Rj9GY3BGZHFGX3FGYnFGP0ZgeUZdb0Zfb0Zib0Zkb0ZfcUZicUY/RmJ5LUYjNidGaXYtRiM2KEZcekZmb0ZdW2xGX3FGYnFGP0ZbeC1GWjYoLUYjNipGZXpGZm9GZ3JGZm9GYVtsRl9xRmJxRj9GYHlGXW9GX29GYm9GZG9GP0ZieS1GIzYnRml2Rl9cbEZpdEZhXGxGP0ZieS1GIzYoRllGZm8tRlo2KC1GIzYoRl1wRmZvLUZecDYlLUZqcTYkLUYjNihGXnJGZm8tRmpxNiQtRiM2KC1GIzYmLUZocjYjLUZaNigtRiM2Ji1GIzYrRml2RmR3Rml0RmZ3Rml0Rl54Rlt4RmN4Rj9GX3FGYnFGP0ZleEZdb0Zfb0Zib0Zkb0Zmb0ZnckY/Rlt4RmVyRlt4Rmd4Rj9GP0Zmb0ZqeEY/Rj9GY3BGZHFGX3FGYnFGP0ZgeUZdb0Zfb0Zib0Zkb0ZfcUZicUY/RmJ5LUYjNidGaXYtRiM2KEZcekZmb0ZpXGxGX3FGYnFGP0ZpdC1GWjYoLUYjNixGZXpGZm9GZ3JGZm9GXXBGZm9GXV1sRl9xRmJxRj9GYHlGXW9GX29GYm9GZG9GP0ZieS1GIzYnRml2RmNebEZbeEZlXmxGP0ZieS1GIzYoRllGZm8tRlo2KC1GIzYmLUZecDYlLUZqcTYkLUYjNidGaXYtRiM2KkZgcEZmb0ZeckZmby1GanE2JC1GIzYoRmddbEZpdEZlckZpdEZneEY/Rj9GZm9GanhGP0ZfcUZicUY/Rj9GY3BGZHFGX3FGYnFGP0ZgeUZdb0Zfb0Zib0Zkb0ZfcUZicUY/RmJ5LUYjNidGaXYtRiM2KEZcekZmb0ZdX2xGX3FGYnFGP0ZbeC1GWjYoLUYjNipGZXpGZm9GZ3JGZm9GYV9sRl9xRmJxRj9GYHlGXW9GX29GYm9GZG9GP0ZieS1GIzYnRml2Rl9gbEZpdEZhYGxGP0ZfcUZicUY/Rl9xRmJxRj8=">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</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" hide-output="false" labelreference="L772" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="A := simplify(d__optimal/(eval(h__1, d = d__optimal)))" display="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">PkkiQUc2Ii1JKXNpbXBsaWZ5RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqJkkrZF9fb3B0aW1hbEdGJCIiIi1JJWV2YWxHRig2JEklaF9fMUdGJC9JImRHRiRGLCEiIg==</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYsKComIiIkIyIiIiIiIyomLCgqJCwmKiZeIyIjPUYnIiQuJkYmRiciJGAjRicjRihGJSIiJiokRiwjRidGJSIkMiIiJDAkRidGJ0YsIyEiIkYlRiZGOSokLCYqJiwoRitGM0Y0ISQ5I0Y3RidGJ0YsRjghIiQqJkYlRiZGKSNGOUYoISUnNCRGJkY5IiIqRidGJywoRiRGJ0Y6RichI0NGJ0Y5</Equation></Text-field>
</Output>
</Group>
<Group hide-input="false" hide-output="false" labelreference="L780" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="evalf(A)" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEmZXZhbGZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSJBRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkBGPUZA">LUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiNJIkFHNiI=</Equation></Text-field>
</Input>
<Output><Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">XiQkIStWOy15WiEiKiQhK20heXZ6JCEjPQ==</Equation></Text-field>
</Output>
</Group>
<Group hide-output="false" labelreference="L807" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group>
</Section>
</Worksheet>