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NCERT Exemplar Solutions Class 10 Mathematics Solutions for Areas related to circles - Exercise 11.4 in Chapter 11 - Areas related to circles

Question 3 Areas related to circles - Exercise 11.4

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

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

= πr2 – πR2

= 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 m2

Hence, the area of the path is 122.46 m2.

Now, Cost of constructing the path per m2 = Rs. 25

∴ cost of constructing 122.46m2 of the path = Rs. 25 × 122.46 = Rs. 3061.50

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