Area Around Circle

In this page area around circle we are going to see some example problems with clear steps.We already know that how to find the area of the circle. In the same thing, we are going to see a different concept here. In these problems we will have two circles. To find the area around the circle we have to subtract the area of the smaller circle from the area of the larger circle.

Example 1:

Find the area of a ring whose outer radius is 20 cm and inner radius is 15 cm respectively.

Solution:

Let "R" be the radius of the outer circle

Lr "r" be the radius of the inner circle

Area of outer circle = ΠR²

Area of outer circle = Πr²

Radius of outer circle (R) = 20 cm

Radius of the inner circle (r) = 15 cm

Area of ring (shaded portion) =Area of outer circle - area of inner circle

                                       = ΠR² -  Πr²

                                       =  Π (R² - r²)

                                       =  Π (20² - 15²)

                                       =  Π x (400 - 225)

                                       =  Π x 175

                                       =  (22/7) x 175

                                       =  22 x 25 

                                       =  550 cm² 

area around circle  area around circle


Example 2:

There is an outside circular path had constructed around a circular garden. If the outer and inner circumferences of the path are 88 cm and 44 cm respectively. Find the width and area of the path.

Solution:

Circumference of outer circle = 88

                                 2ΠR = 88

                   2 x (22/7) x R = 88

                                    R = (88 x 7) /(2 x 22)

                                    R = 2 x 7

                                    R = 14 cm

Circumference of inner circle = 44

                                 2Πr = 44

                   2 x (22/7) x r = 44

                                    R = (44 x 7) /(2 x 22)

                                    R = (2 x 7)/2

                                    R = 7 cm

Width of path = R - r

                   = 14 - 7

                   = 7 cm

Area of outer path = ΠR²

                          = (22/7) x 14²

                          = (22/7) x 14 x 14

                          = 616 cm²   

Area of inner path = Πr²

                          = (22/7) x 7²

                          = (22/7) x 7 x 7

                          = 154 cm²   

Area of path = 616 - 154

                  = 462 cm²                                  


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