A circular pond is 17.5 m in 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.
Cost = \(975\pi\) Rs \(\approx\) Rs 3,064
Step 1: Write down the given information.
Step 2: Find the radius of the pond (inner radius).
Radius \(r = \dfrac{\text{diameter}}{2} = \dfrac{17.5}{2} = 8.75\,\text{m}.\)
Step 3: Find the outer radius (pond + path).
Outer radius \(R = r + \text{width of path} = 8.75 + 2 = 10.75\,\text{m}.\)
Step 4: Area of path = Area of bigger circle – Area of pond.
\( \text{Area} = \pi R^2 - \pi r^2 = \pi(10.75^2 - 8.75^2). \)
Step 5: Simplify the calculation.
\( 10.75^2 = 115.5625, \; 8.75^2 = 76.5625. \)
Difference = \(115.5625 - 76.5625 = 39. \)
So, Area = \( 39\pi \; m^2. \)
Step 6: Find the cost.
Cost = Area × Rate = \(39\pi × 25 = 975\pi\; Rs. \)
Approximating with \(\pi \approx 3.1416,\)
\(975 × 3.1416 ≈ 3,064\; Rs.\)
Final Answer: Cost of constructing the path = Rs 3,064 (approx).