Question

1)A cylinder of radius 12 cm contains water top depth of 20 cm.A spherical iron ball is dropped into the cylinder and the level of water is raised by 6.75 cm. Find the radius of ball.

Answer 1

Given radius of the cylinder, r = 12 cm
It is also given that a spherical iron ball is dropped into the cylinder and the water level raised by 6.75 cm
Hence volume of water displaced = volume of the iron ball
Height of the raised water level, h = 6.75 m
Volume of water displaced = πr2h
= π × 12 × 12 × 6.75 cm3
⇒ Volume of iron ball = π × 12 × 12 × 6.75 cm3 → (1)
But, volume of iron ball =
From (1) and (2) we get

⇒ r3 = 33
∴ r = 9
 Thus the radius of the iron ball is 9 cm