Need help to approach a question of Mensuration

Question

Answered: In a cylinderical vessel of diameter 24 cm filled up with sufficient quantity of water, a solid spherical ball, of radius 6 cm is completely immersed. Then the increases in height of water.

Answer 1

First, you need to find the volume of the sphere, which is equivalent to the volume of water displaced: $$ \frac{4\pi r^3}{3} = \frac{4\pi 6^3}{3} = 288\pi $$ Since the vessel is cylindrical, we can find the increase in height, $h$, using the following formula for the volume of a cylinder: $$ \pi r^2h = V = 288\pi $$