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

Correct Answer:

Option 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 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