# How to find the volume of a cone

## Cone - definition

A cone is a pyramid with a circular cross-section. Hence its base is also circular. It can also be viewed as a borderline case of a pyramid with infinite sides. The cone is a right cone when the point (vertex) is directly above the center of the base and the vertical height h between the base and the point passes through the center of the base. If the apex is offset from the center of the base, the cone is called an oblique cone.

## How to find the volume of a cone

For a cone with a base radius r and a height h , the volume is obtained from the formula:

The result applies to both inclined and right cones. The result is as follows (in this case only the right cone is considered, and the geometry of the oblique cone is slightly more complex than that of the right cone. However, regardless of the position of the vertex, the same results can be obtained):

Consider a cone with a base radius r and a vertical height h , with the center of the base at the origin. If an incremental distance in the y direction is given by dy , the incremental volume in this direction is a circular plate with the thickness dy and the radius x . Therefore, dv = πx 2 dy From the geometry of the cone, (the slope of the slope results) The integral gives the volume of the cone,

Replacing x yields

## Find the volume of a cone - examples

• A right cone has a radius of 10cm at the base and a vertical height of 30cm. Calculate the volume the cone occupies. The radius (r) is 10 cm and the height 30 cm. Hence the volume
• An inclined cone has a diameter of 1 m. If the vertical height is 6 m, find the volume of the cone. 