Question

A lawn is in the shape of a semi-circle of diameter 42 m. The lawn is surrounded by a flower bed of width 7 m all around. Find the area of the flower bed in m² .

Answer 1

Diameter of the inner semi-drde = 42 m 

Hence, radius of the inner semi-circle = r = 21 m 

Width of the flower bed = 7m 

Diameter of the outer semi-circle = ( 42 + 2 x 7) m = 56 m 

Hence, radius of the outer semi-circle= R = 28 m 

Area of the semicircular flower bed =Area of outer semi-cirde - area of inner semi-drde

`= 1/2 pi "R"^2 - 1/2 pi "r"^2`

`= 1/2 pi ("R"^2 - "r"^2)`

`= 1/2 xx 22/7 xx (28^2 - 21^2)`

`= 1/2 xx 22/7 xx (784 - 441)`

`= 1/2 xx 22/7 xx 343`

= 539 m²