Question

A cylinder of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75 cm. Find the radius of the ball. (Use $\mathrm{\pi }=22/7$.

Answer 1

In the given problem, a spherical iron ball is immersed in a water filled cylinder and this leads to a rise in the water level by 6.75 cm. Here, we need to find the radius of the ball.

Given here,

Radius of the cylinder (r_c) = 12 cm

Rise in the level of water in cylinder (h) = 6.75 cm

So, let us take the radius of the spherical ball (r_s) = x cm

Now, according to the problem, the volume of the spherical ball will be equal to the increase in the volume of the cylinder as the volume of water replaced by the ball is increases the level of water in the cylinder.

So,

Volume of the sphere = increase in volume of the water in cylinder

Further,

Therefore the radius of the spherical ball is.