Sia M.

asked • 07/31/17

Im stuck on this problem

A hemispherical container is filled with water, the radius is 12cm. You pour the water into a cylindrical container with a radius of 8cm. Find the water level in cm of the water?

Kendra F.

What's the height of the cylindrical container?
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07/31/17

Kendra F.

oh, nvmd. That's what you want to solve for. I thought for a minute they were looking for 2/3 full or something like that.
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07/31/17

Sia M.

Oops I messed up it's not raidus it's diameter 
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08/01/17

Kendra F.

No problem, just divide the diameter by 2 to get the radius and use that to solve for height.
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08/01/17

1 Expert Answer

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Kendra F. answered • 07/31/17

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A Hemispherical container is a half of a sphere, basically a bowl.
 
The equation for the volume of a sphere is (4/3)πr3
Then half a sphere is (1/2)*(4/3)πr3 = (2/3)πr3
 
r = 12cm for the bowl
Volume of water = (2/3)π(12)3
V(bowl) = 1152π
 
 
The equation for volume of a cylinder = hπr2
1152π = hπ(8)2
1152/82 = h
18 cm = h
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