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:

Given, the circular pond has diameter = 17.5 m

Pond is surrounded by a 2 m wide path.

We have to find the cost of constructing the path at the rate of Rs. 25 per m².

Area of circle = πr²

Radius of pond, r = 17.5/2 = 8.75 m

Area of circular pond = π(8.75)²

= (22/7) (8.75) (8.75)

= (22)(1.25)(8.75)

= 240.625 m²

Radius of the circular pond including the path = 8.75 + 2 = 10.75 m

Area of pond including the path = π(10.75)²

= (22/7)(10.75)(10.75)

= 363.085 m²

Area of the path = area of pond including the path - area of pond

= 363.085- 240.625

= 122.46 m²

Given, rate of construction of the path = Rs. 25 per m²

Rate of constructing 122.46 m² will be

= 122.46 × 25

= Rs. 3061.50

Therefore, the rate of construction of the path is Rs. 3061.50/-

✦ Try This: A circular pond is 12 m is of diameter. It is surrounded by a 3 m wide path. Find the cost of constructing the path at the rate of Rs 35 per m².

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12

NCERT Exemplar Class 10 Maths Exercise 11.4 Problem 5

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

Summary:

A circular pond is 17.5 m is of diameter. It is surrounded by a 2 m wide path. The cost of constructing the path at the rate of Rs 25 per m² is Rs. 3061.50/-

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