# Total surface area of cone formula explained

Learn and know the total surface area of cone formula that comes in mensuration chapter. As a student everyone should learn this formula in math.

We are learning the formula for total surface area of cone, so first we will know what is cone? And then we will know what is the actual meaning of total surface area. Finally we will learn the formula of total surface area.

## What is cone in math?

We can define a cone like this “in right triangle, fixing height and if we rotate the triangle in 360 degrees angle we get a shape called as a cone”. If we observe the base of cone the shape will be “circle”.

### Meaning of total surface area?

In a cone, the total surface area is nothing but the sum of areas of C.S.A of cone and area of base and the area of top face. Generally, we write the total surface area of cone in the short as T.S.A of cone.

#### Formula for total surface area of cone as follows

We have a formula for calculating the total surface area of cone (T.S.A). T.S.A of cone formula is equal to πr ($\ell$ + r). In this formula, π is a constant and approximately equal to $\frac { 22 }{ 7 }$ and “r” is radius of base and finally “$\ell$ ” is slant height of cone. Slant height is given by square root of sum of ${ h }^{ 2 }$ and ${ r }^{ 2 }$ i.e $\ell$= $\sqrt { { h }^{ 2 }+{ r }^{ 2 } }$

Example:

• The radius of cone is given as 7 cm and height is given as 24 cm then find out the T.S.A of cone.

Solution:

As radius and height is given we can find the slant height. Slant height ($\ell$)= square root of sum of ${ 7 }^{ 2 }$ and ${ 24 }^{ 2 }$ = square root of 625 = 25 cm

We know that T.S.A of cone = πr ($\ell$ + r) = $\frac { 22 }{ 7 }$ × 7 (25 + 7) = 22 x 32 = 704 square cm.

• Find the T.S.A of cone if height is 5 m and radius is given as 12 m.

Solution:

Slant height ($\ell$)= square root of sum of 52 and 122 = square root of 169 = 13.

T.S.A of cone = πr ($\ell$ + r) = $\frac { 22 }{ 7 }$ × 12 (13 + 12) = 942.86 sq.cm.