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.

Leave a Comment

Your email address will not be published.