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Question

The inner circumference of a circular track is 440 m, and the track is 14 m wide. Calculate the cost of levelling the track at 25 paise/m2. Also, find the cost of fencing the outer boundary of the track at Rs 5 per metre.

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Solution

Let the radius of the inner circle be r m.
Now,
Inner circumference = 440 m
2πr=440
2×227×r=440r=440×744r=70

We know that the track is 14 m wide.
∴ Outer radius (R) = (70 + 14) = 84 m

Area of the track=π(R2- r2)= π 842-702=227×7056-4900= 6776m2

Cost of levelling at 25 paise per square metre =6676×25=169400 paise
Or,
Rs 169400100= Rs 1694
ā€‹
∴ Outer circumference = 2πR
=2×227×84=528 m

Rate of fencing = 5 per metre
∴ Total cost of fencing =528×5=Rs 2640

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