# Circumference of a Circle | Perimeter of a Circle

## What is the Circumference of a Circle?

The length of a complete circle is called the Circumference of the circle.

## Physical Meaning of Circumference of a Circle

The figure shows the representation of a Circle. As shown in the figure, if we cut the circle at point $P$, and stretch the circle to form a straight line $QR$, then, the length of this straight line is called the Circumference of the circle or the perimeter of the circle.

## How to Find the Circumference of a circle using Diameter?

The formula for finding the Circumference of a circle by using the diameter $AOB$ is given by:

$C = \pi \times AOB$

$C = \pi \times d$

Where, $pi= 3.141592….$ and $d$ is the diameter of the circle.

## How to Find the Circumference of a Circle using Radius?

The relation between the dimeter and the radius of a circle is given by,

$d = 2 \times r$

Where, $d$ is the diameter and $r$ is the radius of the circle.

Therefore, the above equation can be written as,

$C = 2 \times \pi \times r$

## How to Find the Circumference of a Circle from Area?

The Circumference can also be found out from the area of a circle. The formula for finding the Area of a Circle is given by,

$A=\pi\times r^2$

$\therefore\,\,\,\,\, r=\sqrt\frac{A}{\pi}$

Circumference of a Circle is, $C=2\times\pi\times r$

$\therefore\,\,\,\,\, C=2\times\pi\sqrt\frac{A}{\pi}$

$C=2\times \sqrt{{A}\times{\pi}}$

## Circumference of a Circle Formula

The different formulas for finding out the Circumference of a Circle are tabulated below:

## Solved Examples

1. What is the Circumference of a Circle having diameter 5 cm?

Solution: Given, the diameter of the circle, d=5cm
The formula for finding the circumference of a circle using diameter is ,
$C=\pi\times d$
$C=\pi \times 2.5$
$C=3.14\times 2.5$
$C=7.85$ cm
Therefore, the Circumference of the circle is $7.85$ cm.

2. What is the value of R when circumference of circle is 9 metre?

Solution: Given, the circumference of a Circle is $9$ m.
The circumference of a circle is given by:
$C=2\times \pi \times r$
$\therefore\,\,\,\, r=\frac{c}{2\pi}$
$r=\frac{9}{2\times 3.14}$
$r=1.43$ m.
Therefore, the radius of the circle is $1.43$ m.

[WPSM_AC id=3447]

How do you find the circumference of a circle?

The circumference of a circle can be found out by using the formula: $C = \pi \times d$ where $d$ is the diameter of the circle. If the radius $r$ of the circle is given, then circumference can be found out by using the formula: $C = 2 \times \pi \times r$.

What is $\pi$?

The Greek letter $\pi$ is the ratio of the circumference of a circle to its diameter. Mathematically,
$\pi=C/d$

What is the perimeter of a Circle?

The perimeter or circumference of a circle is the complete length of the circle when stretched to form a straight line.

What is the difference between Circumference and Perimeter?

There is no difference between Circumference and Perimeter, both are same.

How many diameters are there for a circle?

There are infinite number of diameters for a given circle.