Circumference of a Circle | Perimeter of Circle

Circumference of a Circle

The curved boundary or rim of a circle which is equidistant from its centre is called circumference of a circle. The circumference of a circle is also known as the perimeter of circle. 

In the given figure curve line ABCD is the circumference of the circle. It is generally denoted by letter C.

Let us do an experiment. Take a coin. Put it on the scale and roll it as shown in the figure below. 

When rolling completes one round it travels the length equal to the circumference of the coin. Repeat this activity for other circular objects.

In such activity, if diameter of the object is 3.5 cm then circumference is 11 cm. If diameter is 7 cm then circumference is 22cm. Similarly, if diameter is 14 cm them circumference is 44cm. From the above measurements, we have found that.

                   11/3.5 = 22/7 = 44/14 = 3.14

The length of the diameter of different circles are proportional to their respective circumference. This constant ratio of circumference by diameter (C/d) = 3.14 is denoted by Greek symbol π (pai). For our convenience we use, π = 22/7 = 3.14

or,      C/d = π

or,      C = πd

or,      C = π × 2r  [∵ d = 2r]

or,      C = 2πr

∴  C = πd  or C = 2πr  is the formula to calculate the circumference of a circle in terms of radius or diameter.

 

Workout Examples

Example 1: Find the circumference of the circle having

a)   diameter = 14 cm

b)  radius = 3.5 cm

Solution: a) Here,

                   Diameter (d) = 14 cm

                   Circumference (c) = ?

                   We know,

                             C = πd = 22/7 × 14 cm = 44 cm

                   b) Here,

                   Radius (r) = 3.5 cm

                   Circumference (c) = ?

                   We know,

                             C = 2πr = 2 × 22/7 × 3.5 cm = 22 cm

 

Example 2: Find the radius of the circle whose circumference is 88 cm.

Solution: Here,

                   Circumference (c) = 88 cm

                   Radius (r) = ?

                   We know,

                             C = 2πr

                   i.e.     88 = 2 × 22/7 × r

                   or,     88 = 44/7 × r

                   or,     88 × 7/44 = r

                   or,     r = 14 cm

 

Example 3: The radius of circular cricket ground is 35 m. Find the length of rope which is required to fence around it 3 times?

Solution: Here,

                   Radius (r) = 35 m

                   Circumference (c) = ?

                   We know,

                             C = 2πr

                                = 2 × 22/7 × 35 m

                                = 220 m

                   ∴ 1 round = 220 m

                   ∴ 3 round = 3 × 220 m = 660 m

                   ∴ 660 m long rope is required to fence around the cricket ground 3 times.

 

You can comment your questions or problems regarding the circumference or perimeter of a circle here.