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Volume of a Cone

A cone is a three-dimensional figure with one circular base. A curved surface connects the base and the vertex.

Math diagram

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 , et cetera).  Be sure that all of the measurements are in the same unit 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 .

V = 1 3 B h or V = 1 3 π r 2 h , where B = π r 2

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.


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

Math diagram


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 π r 2 h

Substitute 8 for r and 18 for h .

V = 1 3 π ( 8 ) 2 ( 18 )


V = 1 3 π ( 64 ) ( 18 ) = 384 π 1206.4

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


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