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Question
A lawn is in the shape of a semicircle of diameter 42m. the lawn is surrounded by a flower bed of width 7m all round. Find the area of the flower bed in m2.
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Solution
There are two concentric semi circles. The diameter of the inner circle = 42 or radius, a = 21m. The radius of the outer circle, b = 21 + 7 = 28m.
Because the radius of a Circle with diameter d is r = `"d"/(2)`
The Area of the inner Semi-circle with radius a = `(pi"a"^2)/(2) = (pi21^2)/(2)`
∴ The Area of the outer Semi-circle with radius b = `(pi"b"^2)/(2) = (pi28^2)/(2)`
and The Area of a Semi-circle with radius r = `(pi"r"^2)/(2)`
The Area of the flower bed
= `(pi28^2)/(2) - (pi21^2)/(2)`
= `pi/(2)(28^2 - 21^2)`
= `pi/(2)(784 - 441)`
= `pi/(2)(343)`
= `(22)/(7 xx 2)(343)`
= 539m2.
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