# Volume of a Cone

The volume of a right circular cone is one-third of the volume of a right circular cylinder of the same base and same height.

If is the height of the cone and is the radius of the base, then

(as the area of the base )

**Rule: **The volume of a cone equals the area of the base times one-third the altitude.

__Example__:

The circumference of the base of a m high conical tent is m. Find the volume of the air contained in it.

__Solution__:

Circumference of the base m

m

height of the conical tent m

volume of air

cubic m

__Example__:

The vertical height of a conical tent is dm and the diameter of its base is m. Find the number of people it can accommodate if each person is to be allowed cubic dm of space.

__Solution__:

** **Here height dm

Diameter m dm

Radius dm

Volume

Cubic dm

Space allowed for person cubic dm

the required number of people people