# Area of circle formula with examples explained

Learn and know what is the area of circle formula. All of us know what is a circle and the important terms related to circle i.e. diameter, radius, chord, perimeter, sector, and secant and so on. In this one more important term is area.

Now we will learn how to find the area of circle. For this we have a formula. So now we will learn the area of circle formula. Don’t worry the formula is very simple and easy to remember. Just read and write the formula 4 or 5 times, automatically you can remember it.

## Area of circle formula as follows:

The formula for finding the area of a circle is given by  A = π ${ r }^{ 2 }$

“π” We have a standard value i.e. $\frac { 22 }{ 7 }$ or 3.14 and “r” means radius of circle.

Note:

Area of circle formula can also be written in terms of diameter also. For this we need to replace “r” with $\frac { d }{ 2 }$ in the above formula.

Suppose if radius is 1 unit then the circle becomes unit circle.

### Example Problems:

♦ Calculate the area of a circle when radius is 49 cm.

Solution:

Given

We know that,

A = π ${ r }^{ 2 }$

A = $\frac { 22 }{ 7 }$ × ${ 49 }^{ 2 }$

A = $\frac { 22 }{ 7 }$ × 49 × 49

A = 22 × 7 × 49

A = 7546 ${ cm }^{ 2 }$

♦ If the diameter of a circle is given as 28 cm then find the area of a circle.

Solution:

Given

Diameter = 28 cm.

Radius = $\frac { d }{ 2 }$ = $\frac { 28 }{ 2 }$ = 14 cm.

We know that,

A = π ${ r }^{ 2 }$

A = $\frac { 22 }{ 7 }$ × ${ 14 }^{ 2 }$

A = $\frac { 22 }{ 7 }$ × 14 × 14

A = 22 × 2 × 14

A = 616 ${ cm }^{ 2 }$

♦ The area of a circle is 1386 ${ m }^{ 2 }$. Find the radius of the circle.

Solution:

Given

Area = 1386 ${ m }^{ 2 }$

We know that,

A = π ${ r }^{ 2 }$

1386   = $\frac { 22 }{ 7 }$  ${ r }^{ 2 }$

1386 × $\frac { 7 }{ 22 }$ = ${ r }^{ 2 }$

$\frac { 9702 }{ 22 }$ = ${ r }^{ 2 }$

441 = ${ r }^{ 2 }$

${ 21 }^{ 2 }$ = ${ r }^{ 2 }$

21 = r

Therefore, radius of a circle is 21 m.

I hope you understood area of circle formula and the example problems based on it.