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Question
A circular pond is 17.5 m is of diameter. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs 25 per m2.
Solution
Radius of the circular pond r1 = `17.5/2` m = 8.75 m
Width of path = 2 m
∴ Radius of the path including pond
r2 = 8.75 + 2 = 10.75 m
Area of path = `pi"r"_2^2 - pi"r"_1^2 = pi["r"_2^2 - "r"_1^2]`
Cost of constructing the path = Rs 25 `pi("r"_2^2 - "r"_1^2)`
∴ Required cost = Rs `25 xx 22/7 [(10.75)^2 - (8.75)^2]`
= `25 xx 22/7 [10.75 - 8.75][10.75 + 8.75]`
= `25 xx 22/7 xx 2 xx 19.5`
= `(50 xx 22 xx 19.5)/7`
= `(1100 xx 19.5)/7`
= `21450/7`
= Rs. 3064.29
Hence, the cost of constructing path is Rs 3064.29
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