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 -dimensional solid is the amount of space it occupies. Volume is measured in cubic units ( et cetera). Be sure that all of the measurements are in the same unit before computing the volume.
The volume of a cone with radius is one-third the area of the base times the height .
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.
From the figure, the radius of the cone is cm and the height is cm.
The formula for the volume of a cone is,
Substitute for and for .
Therefore, the volume of the cone is about cubic centimeters.