Question

a cylinder of radius 12cm contains water to a depth of 20cm. an iron ball is dropped in it of radius 9cm.find the rise in level of water

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