Question

A sphere of radius 6 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 8 cm. If the sphere is submerged completely, then the surface of the water rises by

Options

• 4.5 cm

• 3

• 4 cm

• 2 cm

Answer 1

Radius of the sphere = 6 cm.

Volume of the sphere

`=4/3pir^3`

`=4/3 pi xx 6 xx 6 xx 6`

and

Radius of the cylinder = 8 cm

Volume of the cylinder

`=pir^2h`

`=pi xx 8 xx 8 xx h`

Therefore,

Volume of the sphere = volume of the cylinder

`4/3pi(6)^3 = pi(8)^2 h`

or

`h = (4 xx 72)/64 = 4.5 cm`