Table of Contents

## 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:

Serial No. | Description | Formula |

1 | Circumference using Diameter | C = \pi \times d |

2 | Circumference Using Radius | C = 2 \times \pi \times r |

3 | Circumference from Area | C=2\times \sqrt{{A}\times{\pi}} |

## 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.

## Frequently Asked Questions

[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.

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