SOLUTION: I'm trying to help my daughter with her science fair project. Her project was to find out if 3 different shaped containers(we used cylinder, round and square)with the same volume

Algebra ->  Volume -> SOLUTION: I'm trying to help my daughter with her science fair project. Her project was to find out if 3 different shaped containers(we used cylinder, round and square)with the same volume       Log On


   

Question 141257: I'm trying to help my daughter with her science fair project. Her project was to find out if 3 different shaped containers(we used cylinder, round and square)with the same volume of water (355ml) in each, then frozen, would melt at the same or different speeds. I know that the one with the larger surface area will melt faster but what I'm not sure of is how to find out the surface area of each container. I didn't think it would be accurate to use the traditional surface area formula, measuring the container since the container isn't filled all the way. Hope this makes sense.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
You MUST fill the containers completely.
They must be frozen in the same space so they are at the same temp.
.
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)
.
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.
.
With the above measurements you can construct your containers.
You might make them out of clay.
.
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
.
The sphere should melt last.
.
Good luck with your adventure!
.
Ed