# Spherical Shell

A solid enclosed between two concentric spheres is called a spherical shell. For a spherical shell, if and are the outer and inner radii respectively, then the volume of the shell is

Or

__Example__:

A sphere of radius **5cm** is dropped into a cylindrical vessel partly filled with water. The diameter of the vessel is **10cm**. If the sphere is completely submerged, how much will the water rise?

__Solution__:

The sphere will displace a volume of water equal to that of itself, and this shows how much the water will rise.

Volume of sphere **cu.cm**

The radius of the cylindrical vessel **cm**

The volume height occupied by **cu.cm.** of water in a cylindrical vessel of **5cm** radius

**cm**

__Example__:

A solid cylinder of glass, the radius of whose base is **9cm** and height is **12cm**, is melted and turned into a sphere. Find the radius of the sphere which is formed.

__Solution__:

Volume of the cylinder

**cu.cm **--- (1)

Volume of the sphere --- (2)

By the given condition,

(1) = (2)