**Volume of a Cone**

A cone is a three-dimensional figure with one circular base. A curved surface connects the base and the vertex. The volume of a 3 -dimensional solid is the amount of space it occupies. Volume is measured in cubic units ( in^{3}, ft^{3}, cm^{3}, m^{3} etc cetera).

**The volume of a cone is: 1/3(Area of Base)(height) = 1/3 π r ^{2} h**

The volumes of a cone and a cylinder are related in the same way as the volumes of a pyramid and a prism are related. If the heights of a cone and a cylinder are equal, then the volume of the cylinder is three times as much as the volume of a cone.

**Example:**

Find the volume of the cone shown. Round to the nearest tenth of a cubic centimeter.

**Solution**

From the figure, the radius of the cone is 8 cm and the height is 18 cm.

The formula for the volume of a cone is, V = 1/3 πr^{2} h

Substitute 8 for r and 18 for h.

V = 1/3 (3.1416) (8)^{2} (18)

≈ 1206.4

Therefore, the volume of the cone is about 1206.4 cubic centimeters.

**Information Source: Varsity Tutors**