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**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 m ^{2}**

Answer:

Diameter of the circular pond = 17.5 m

Let r be the radius of the park = (17.5/2) m = 8.75 m

According to the question,

The circular pond is surrounded by a path of width 2 m.

So, Radius of the outer circle = R = (8.75+2) m = 10.75 m

Area of the road = Area of the outer circular path – Area of the circular pond

= πr^{2} – πR^{2}

= 3.14 × (10.75)^{2} – 3.14 × (8.75)^{2}

= 3.14 × ((10.75)^{2} – (8.75)^{2})

= 3.14 × ((10.75 + 8.75) × (10.75 – 8.75))

= 3.14 × 19.5 × 2 = 122.46 m^{2}

Hence, the area of the path is 122.46 m^{2}.

Now, Cost of constructing the path per m^{2} = Rs. 25

∴ cost of constructing 122.46m^{2} of the path = Rs. 25 × 122.46 = Rs. 3061.50

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