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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?

Options

A) 12cm

B) 1cm

C) 3cm

D) 6cm


The correct answer is D.

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


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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