Volume of Cone – Formula and Examples

Cone

A circular or elliptical base, a vertex lying outside the plane of the base, and all the lines joining points on the edge of the base to the vertex. The vertex is sometimes called the apex. If the base is a circle, it is called a circular cone.

If the line from the centre of the base to the vertex is perpendicular to the base. It is called a right cone, and the line is called the axis.

Examples: Solids like ice-cream cones, conical tents, funnels etc, are having the shape of cone.

Volume of a cone

A cone with height h and base radius r.

Then we have:

The volume of a cone = (1/3) πr²h cubic units

Where,

‘r’ is the base radius of the cone

‘l’ is the slant height of a cone

‘h’ is the height  of the cone

Solved Examples of Cone

Example.1: Calculate the volume of cone, if r= 3 cm and h= 6 cm.

Solution:

Given:

r = 3

h= 6

By Using the Volume of Cone formula

The volume of a cone = (1/3) πr²h cubic units

V= (1/3) × 3.14 × 3² ×6

volume = (1/3) × 3.14 × 9 ×6

V= (1/3) × 3.14 × 54

V = 56.52 cm³

Therefore, the volume of a cone =56.52 cubic units.

Example.2: If the height of a given cone is 5 cm and the diameter of the circular base is 8 cm. Then find its volume.

Solution: Diameter of the circular base = 8 cm.

So, radius = 8/2 = 4 cm

Height = 5 cm

By the formula of cone volume, we know;

So by putting the values of r and h, we get;

V = 1/3 π 4² 5

Since π = 22/7

Therefore,

V = 1/3 x 22/7 x 16 x 5

V = 83.80 cu.cm.