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Sphere and Cylonder problem

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by AndyB » Sun Oct 09, 2011 3:35 am
Hello Everyone,

Anybody!!! Please help me in solving the below problem.

Q) A sphere with a diameter of 6cm is dropped in a circular cylindrical vessel that is partially filled with water.The diameter of the cylindrical vessel is 12 cm.If the

sphere is completely submerged in water how much will the level of water rise in lthe cylindirical vessel.

a)1 cm
b)2 cm
c)3 cm
d)4 cm
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by Anurag@Gurome » Sun Oct 09, 2011 3:47 am
AndyB wrote:A sphere with a diameter of 6cm is dropped in a circular cylindrical vessel that is partially filled with water.The diameter of the cylindrical vessel is 12 cm.If the sphere is completely submerged in water how much will the level of water rise in lthe cylindirical vessel.
Volume of the sphere = (4/3)*pi*(6/2)^3 = 36*pi cc

Say, the level of the water in the sphere rises by h cm.
Hence, the sphere replaces pi*[(12/2)^2]*h = 36*pi*h cc of water.

Therefore, 36*pi = 36*pi*h ---> h = 1

The correct answer is A.
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by parul9 » Sun Oct 09, 2011 5:31 am
The water in cylinder will be displaced to accommodate the volume of the sphere.
So, volume of sphere = volume of displaced water in cylinder.

4/3*pi*3^3 = pi*6^2*h, where h is the height by which the water level will rise.

this gives us h = 1 cm.

So, A
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