# 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 units are in units cubed (in3 , ft3 , cm3 , m3 , et cetera).  Be sure that all of the measurements are in the same units before computing the volume.

The volume V of a cone with radius r is one-third the area of the base B times the height h .

Note : The formula for the volume of an oblique cone is the same as that of a right one.

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,

Substitute 8 for r and 18 for h .

Simplify.

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