Area of Circle

Area of Circle

Area of Circle

Total surface on the plane covered by the circumference of a circle is termed as the area of circle. Area of circle is given by the formula Area = πr2 where r is the radius of the circle. This formula can be understood and derived by the following activities.

Activities to derive the formula for area of circle

1.       Take a circular shaped paper.

2.       Cut the circle into two equal halves.

3.       Cut each half further into small pieces equally as you can see in the figure.

4.       Arrange  the pieces of two halves in one place to form like a rectangle as shown in the figure.

5.       As we go on increasing the number of small pieces it will tend to be a rectangle PQRS of length = half of circumference (c/2) and breadth = radius (r).

We know, circumference of the circle (c) = 2πr

        Length of rectangle (l) = C/2 = 2πr/2 = πr

          Breadth of rectangle (b) = r

Now,

          Area of circle = Area of rectangle PQRS

                             = length × breadth

                             = πr × r

                             = πr2 

Area of circle = πr2


Workout Examples

Example 1: Find the area of the circle having diameter of 14 cm.

Solution: Here,

                   Diameter (d) = 14 cm

                   Radius (r) = d/2 = 14/2 = 7 cm

                   We know,

                   Area of circle = πr2

                                       = 22/7 × 72

                                       = 22/7 × 49

                                       = 154 cm2

 

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

Solution: Here,

                   Circumference (C) = 88 cm

                    i.e.     2πr = 88

                   or,     2 × 22/7 × r = 88

                   or,     44/7 × r = 88

                   or,     r = 88 × 7/44

                   or,     r = 14 cm

                   We know,

                   Area of circle = πr2

                                    = 22/7 × 142

                                    = 22/7 × 196

                                    = 616 cm2

 

Example 3: If the area of a circle is 154 cm2, then finds its circumference.

Solution: Here,

                   Area of circle (A) = 154 cm2

                   i.e.     πr2 = 154

                   or,     22/7 × r2 = 154

                   or,     r2 = 154 × 7/22

                   or,     r2 = 49

                   or,     r2 = 72

                   or,     r = 7 cm

                   Now,

                   Circumference  of circle = 2πr

                                               = 2 × 22/7 × 7

                                               = 44 cm

 

Example 4: Find the area of the shaded region of the figure.

Find the area of the shaded region

Solution: Here,

                   Side of square (l) = 8 cm

                   Area of square (A1) = l2

                                          = (8 cm)2

                                          = 64 cm2

                   Radius of quarter circle (r) = 8/2 = 4 cm

                   Area of 4 quarter circles (A2) = Area of one full circle

                                                        = πr2

                                                        = 22/7 × 42

                                                        = 50.28 cm2

                   Area of shaded region (A) =  A1 – A2

                                                      = 64 cm2 – 50.28 cm2

                                                      = 13.72 cm2


 Example 5: Find the area of the shaded region of the figure.

Find the area of the shaded region

Solution: Here,

                   Length of rectangle (l) = 14 cm

                   Breadth of rectangle (b) = 7 cm

                   Area of rectangle (A1) = l × b

                                              = 14 cm × 7 cm

                                              = 98 cm2               

                   Radius of each half circle (r) = 7/2 = 3.5 cm

                   Area of 4 half circles (A2) = Area of two full circle

                                                 = 2 × πr2

                                                 = 2 × 22/7 × (3.5)2

                                                 = 77 cm2

                   Area of shaded region (A) =  A1 – A2

                                                      = 98 cm2 – 77 cm2

                                                      = 21 cm2

 

You can comment your questions or problems regarding the area of circle here.


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