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If a spherical metal bob of radius 3cm is fully immersed in a cylinder containin...

Question

If a spherical metal bob of radius 3cm is fully immersed in a cylinder containing water and the water level rises by 1cm, what is the radius of the cylinder?

A) 12cm

B) 1cm

C) 3cm

D) 6cm

Explanation:

If the bob is fully immersed in the water, then the volume of water displaced will be equal to the volume of the bob = 4/3πr3, where r is the radius of the bob.
This volume of water in the cylinder = πr2l, where r = radius of the cylinder, and l = level of water rose in the cylinder.

Therefore, π x r2 x l = 4/3 x π x 33

Then r2 = 36
r = √36
r = 6cm

Dicussion (1)

• If the bob is fully immersed in the water, then the volume of water displaced will be equal to the volume of the bob = 4/3πr3, where r is the radius of the bob.
This volume of water in the cylinder = πr2l, where r = radius of the cylinder, and l = level of water rose in the cylinder.

Therefore, π x r2 x l = 4/3 x π x 33

Then r2 = 36
r = √36
r = 6cm