Question 141257
You MUST fill the containers completely.
They must be frozen in the same space so they are at the same temp.
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Sphere:
V=(4pi*r^3)/3
355=(4pi*r^3)/3
355*3=4pi*r^3
1065/4=pi*r^3
266.25=pi*r^3
r^3=266.25/pi
r^3=84.75...
r=4.39... cm
d=8.8... cm. (diameter of the sphere)
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Cube:
s^3=V
s^3=355
s=7.0... cm (length of a side of the cube)
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Cylinder:
pi*r^2*h=V
Let the height be 10 cm
pi*r^2*10=355
pi*r^2=355/10=35.5
r^2=35.5/pi=11.3...
r=3.36
d=6.7...cm.
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With the above measurements you can construct your containers.
You might make them out of clay.
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Surface Areas:
Sphere:
4pi*r^2
4pi*4.39^2=242 cm^2
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Cube:
49*6=294 cm^2
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Cylinder:
2pi*r*h+2pi*r^2
=2pi*3.36*10 + 2pi*3.36^2
=211+71
=282 cm^2
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The sphere should melt last.
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Good luck with your adventure!
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Ed