CIRCUMFERENCE OF A CIRCLE

Circumference of a circle is the distance around the circle. 

Formula :

Circumference of Circle = 2πr

Here the value of π is either 22/7 or 3.14 and "r" stands for radius of a circle.

Example 1:

Find the circumference of a circle whose radius is 14 cm.

Solution:

Formula for circumference of circle is

=  2πr

Substitute π = 22/7 and r = 14.   

≈  2 x (22/7) x 14

=  2 x 22 x 2

=  88

So, circumference of the given circle is about 88 cm. 

Example 2:

Find the diameter of circle with circumference is 88 cm.

Solution:

Circumference of circle  =  88 cm

2πr  =  42

2 x (22/7) x r  =  42

(44/7) x r  =  42

Multiply each side by 7/44.

r  =  88 x (7/44)

r  =  2 x 7

r  =  14

Then, diameter is 

=  2 x radius

=  2 x 14

=  28 cm

Example 3 :

Find the circumference of a circle with an area of 441π square feet. 

Solution :

Area of the circle  =  441π ft²

πr²  =  441π

Divide each side by π.

r²  =  441

r  =  21

Formula for circumference of circle is

=  2πr

Substitute π = 22/7 and r = 21.

≈  2 x (22/7) x 21

=   2 x 22 x 3

=  132

So, circumference of the given circle is about 132 ft. 

Example 4 :

The moon is about 384000 km away from the earth and its path around the earth is nearly circular. Find the distance traveled by the moon every month.

Solution :

Because the path of the moon around the earth is nearly circle, the distance traveled by the moon every month is the circumference of the circle. 

Given : The moon is about 384000 km away from the earth

Then radius is 384,000. 

Formula for circumference of circle is

=  2πr

Substitute π = 22/7 and r = 38400.   

≈  2 x 3.14 x 384,000

=  2,411,520

So, the distance traveled by the moon every month is about 2,411,520 km. 

Example 5 :

A copper wire is in the form of a circle with radius 35 cm. If it is bent into a square, find the length of each side of the square.

Solution :

Given : Radius of a circle is 35 cm.

Since the same wire is bent into the form of a square,

Circumference of the circle  =  Perimeter of the square

Circumference of circle is

=  2πr

Substitute π = 22/7 and r = 35.   

≈  2 x (22/7) x 35

=  2 x 22 x 5

=  220

Then,

perimeter of the square  =  220 cm

4a  =  220

Divide each side by 4.

a  =  55

So, the length of each side of the square is 55 cm. 

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