Question

A cylinder of radius 12 cm contains water up to the height 20 cm. A spherical iron ball is dropped into the cylinder and thus water level raised by 6.75 cm. What is the radius of iron ball?

Answer 1

Given:

Radius of cylinder = 12 cm = r₁

Water level in cylinder = 20 cm

On dropping sphere ball, rise in height = 6.75 cm = h

Radius of sphere = r₂

Now, Volume of water raised in cylinder = Volume of the sphere

⇒ `pir_1^2h = 4/3 pir_2^3`

⇒ `(12 xx 12 xx 6.75) = 4/3 r_2^3`

⇒ r₂³ = 729

Taking cube root on both sides,

r₂ = 9 cm

∴ The radius of the iron ball is 9 cm.