AREA OF A CIRCLE

Area of a circle stands for surface occupied by the circle.

In the above shape, the part filled with red color is called area of the circle.

Formula :

Area of Circle  =  πr²

Here the value of π is approximately 22/7 or 3.14 and 'r' is known as the radius of the circle.

Example 1 :

Find the area of the circle which is having the radius 21 cm.

Solution :

Formula for area of circle is

=  πr²

Substitute π = 22/7 and r = 21.

≈  (22/7 ) x 21²

=  (22/7) x 21 x 21 

=  22 x 3 x 21

=  1386

So, area of the given circle is about 1386 square cm. 

Example 2 :

Find the area of the circle which is having the diameter 28 cm.

Solution :

Given : Diameter  =  28 cm

Then, radius is 

=  diameter/2  

=  28/2

 =  14 cm

Formula for area of circle is

=  πr²

Substitute π = 22/7 and r = 14.

≈  (22/7 ) x 14²

=  (22/7) x 14 x 14

=  22 x 2 x 14

 =  616

So, area of the given circle is about 616 square cm. 

Example 3 :

If the area of a circular region is 3850 cm², then find its diameter.

Solution :

Area of the circular region  =  616 cm²

  πr²  =  616

 (22/7)r²  =  616

Multiply each side by 7/22.

r²  =  616 x 7/22

  r²  =  28 x 7

r²  =  196

r  =  14 cm

Then, diameter is 

=  2 x radius

=  2 x 14

=  28 cm

Example 4 :

Find the area of a circle with a circumference of 28π feet. 

Solution :

Circumference of the circle  =  28π ft

2πr  =  28π

Divide each side by 2π.

r  =  14

Formula for area of circle is

=  πr²

Substitute π = 22/7 and r = 14.

≈  (22/7) x 14²

=   (22/7) x 14 x 14

=  22 x 2 x 14

=  616

So, area of the given circle is about 616 square ft. 

Example 5 :

Find the length of the rope by which a goat must be tethered in order that it may be able to graze an area of 9856 square meters. 

Solution :

The area that the goat grazes will be in the shape of a circle. Then the length of the rope by which the goat is tethered will be radius.

It is given that the area that the goat grazes is 9856 square meters.  

Then, 

πr²  =  9856

Substitute π =  22/7.

 (22/7) x r²  =  9856

Multiply each side by 7/22.

r²  =  9856 x 7/22 

r²  =  448 x 7

r²  =  3136

r  =  56

So, the length of the rope by which a goat must be tethered is 56 meters. 

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