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Question
The circumference of a given circular park is 55 m. It is surrounded by a path of uniform width of 3.5 m. Find the area of the path.
Solution
Let r be the radius of the circular park.
2πr = 55
r = `55/2π`
= 8.75 m
area of the park = π x ( 8.75 )2 = 240.625 m2
Radius of the outer circular region including the path is given by
R = 8.75 + 3.5
= 12.25 m
Area of that circular region is A = π x ( 12.25 )2 = 471.625 m2
Hence area of the path is given by
Area of the path = 471.625 - 240.625 = 231 m2.
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