Question

A solid is in the shape of a hemisphere of radius 7 cm, surmounted by a cone of height 4 cm. The solid is immersed completely in a cylindrical container filled with water to a certain height. If the radius of the cylinder is 14 cm, find the rise in the water level.

Answer 1

Volume of solid = `1/3πr^2h + 2/3πr^3`

= `1/3πr^2 (h + 2r)`

= `π/3 xx (7)^2 xx (4 + 2 xx 7)`

= `π/3 xx 49 xx 18`

= 294π cm³

Let y be the height rise of water in a cylindrical cylinder with radius R = 14 cm.

∴ Volume of water rise in a cylindrical container = Volume of solid immersed

πR²y = 294π

`\implies` π(14)²y = 294π

∴ y = `294/(14 xx 14)`

= `21/14`

= `3/2`

= 1.5 cm

Hence, The rise in the water level is y = 1.5 cm