Question

# A circular pond is 17.5 m is of diameter. It is surrounded by a 2m wide path . Find the cost of constructing the path at the rate of ₹25 per m2

A

₹3000

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B

₹2500

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C

₹3061

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D

₹1058

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Solution

## The correct option is C ₹3061 Given that a circular pond is surrounded by a wide path. The diameter of circular pond = 17.5 m ∴ Radius of circular pond (r1)=Diameter2 i.e OA=r1=17.52=8.75m and the width of the path = 2m i.e AB = 2m Now, Length of OB=OA+AB=r1+AB Let (re)=8.75+2=10.75m So, area of circular path = Area of outer circle i.e ( circular pond + path) - Area of circular pond =πr2e−πr21 =π(r2e−r21) =π{(10.75)2−(8.75)2} =π{(10.75+8.75)(10.75−8.75)} =122.46 m2 Now, cost of constructing the path per square metre =₹25 ∴ Cost of constructing the path = area of the path × cost of constructing the path per square meter = ₹122.46 m2=122.46×25 =₹3061.50 Hence, required cost of constructing the path at the rate of ₹25 per m2 is ₹3061

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