# Formula for Volume of Cone with Examples

Here you will learn what is the formula for volume of cone and examples based on it.

Let’s begin –

## What is Cone ?

A cone is a solid which has a circle at its base and a slanting lateral surface that converges at the apex. Its dimensions are defined by the radius of the base (r), the height (h) and the slant height (l).

Also Read : Surface Area of Cone – Formula & Examples

## Formula for Volume of Cone

Volume of Cone = $$1\over 3$$ $$\pi r^2 h$$

where r is the base radius and h is the height of the cone.

ExampleThe height and the slant height of a cone are 21 cm and 28 cm respectively. Find the volume of the cone.

Solution : Here h = 21 and $$l$$ = 28

We know that, $$l^2$$ = $$r^2$$ + $$h^2$$

$$\implies$$ $$r^2$$ = $$l^2$$ – $$h^2$$

$$\implies$$ r = $$\sqrt{ 28^2 – 21^2}$$ = $$7\sqrt{7}$$

So, Volume of the Cone = $$1\over 3$$ $$\pi r^2 h$$

= $$1\over 3$$ $$\pi \times 343 \times 21$$

= 7546 $$cm^3$$

Example : In a marriage ceremony of her daughter Poonam, Ashok has to make arrangements for the accommodation of 150 persons. For this purpose, he plans to build a conical tent in such a way that each person has 4 sq. meters of the space on ground and 20 cubic meters of air to breath. What should be the height of the conical tent ?

Solution : Let the height of the conical tent = h metre.

Radius of the base of the cone = r meter.

The tent has to accommodate 150 persons.

The space required by each person on the ground = 4 $$m^2$$

And the amount of air = 20 $$m^3$$

$$\therefore$$  Area of the base = 150 $$\times$$ 4 = 600 $$m^2$$

$$\implies$$   $$\pi r^2$$ = 600 $$\implies$$ r = 13.817 m

Volume of the air required for 150 persons = 150 $$\times$$ 20 = 3000 $$m^3$$

$$\implies$$  $$1\over 3$$ $$\pi r^2 h$$ = 3000 $$m^3$$

$$\implies$$ h = $$3000 \times 7 \times 3\over 22 \times (13.817)^2$$ = 15 m

Hence the height of the conical tent is 15 m.