## AREA OF A CIRCLE

Area of a circle :

Area of the circle stands for surface occupied by the figure. In the above shape, the part filled with red color is called area of a circle.

Formula :

Area = Π r ²

Here the value of Π is either 22/7 or 3.14 and "r" is known as the radius of a circle. Now let us see some example problems.

Example 1:

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

Solution :

In this problem we need to find the area of the circle having a radius 21 cm. We need to apply this value instead of r in the formula.

Area of circle  =  Π r ²

=  (22/7 ) x ( 21 )²

=  (22/7) x 21 x 21

=  22 x 3 x 21

=  66 x 21

=  1386 cm²

Hence the area of the given circle is 1386 cm²

Example 2:

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

Solution :

To find the area first we need to find the radius of the circle from the diameter.

Diameter  =  28 cm

=  28/2

=  14 cm

Area of circle = Π r ²

=  (22/7)  (14)²

=  (22/7)  14 ⋅ 14

=  22  2  14

=  44  14

=  616 cm²

Example 3 :

The area of a circular region is 616 cm². Then find its diameter.

Solution :

Area of circle = 616 cm²

Π r ² = 616 cm²

(22/7)   r² = 616

r²  =  (616  7) /22

r²  =  (616  7) /22

r²  =  28   7

r  =  √(2    7)

r  =  2  7

r  =  14 cm

=  2  14

=  28 cm

Hence the diameter of the given circle is 28 cm.

Example 4 :

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

Solution :

In this problem we need to find the area of the circle having a radius 21 cm. We need to apply this value instead of r in the formula.

Area of circle = Π r ²

=  (22/7)  ( 21 )²

=  (22/7)  21 ⋅ 21

=  22  3  21

=  66  21

=  1386 cm²

Hence area of the given circle is 1386 cm²

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