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.

Circumference of a 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.DescriptionFormula
1Circumference using DiameterC = \pi  \times d
2Circumference Using RadiusC = 2 \times \pi  \times r
3Circumference from AreaC=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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