AREA OF A CIRCLE

About "Area of a circle"

Area of a circle :

In this section, we are going to see how to find the area of a circle. This page contains formulas, example problems and also practice questions to understand this topic in a better way.

Area :

Area of the circle means surface occupied by the figure.

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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

Therefore 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

Radius = diameter/2

          = 28/2

          = 14 cm

Area of circle = Π r ²

                   =  ( 22/7 )  x (14)²

                   = ( 22/7 )  x 14 x 14

                   = 22 x 2 x 14

                   = 44 x 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)  x r² = 616

                  r² = (616 x 7) /22

                  r² = (616 x 7) /22

                  r² = 28 x 7

                  r² = √(2 x 2 x 7 x 7)

                  r = 2 x 7

                  r = 14 cm

Diameter = 2 x radius

             = 2 x 14

             = 28 cm

Therefore 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 ) x ( 21 )²

                   = (22/7) x 21 x 21 

                   = 22 x 3 x 21

                   = 66 x 21

                   = 1386 cm²

Therefore the area of the given circle is 1386 cm²

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