Question

A circular park, 42 m in diameter, has a path 3.5 m wide running around it on the outside. Find the cost of gravelling the path at Rs. 4 per m²

• A. Rs. 1672
• B. Rs. 1652
• C. Rs. 1802
• D. Rs. 2048

Hint:

For circular areas, use the formula \( \pi r^2 \) to calculate the area, and subtract the inner area from the outer area to find the path's area.

Answer 1

The Correct Option is C

Radius of the park = \( \frac{42}{2} = 21 \, \text{m} \) The radius of the outer edge of the path = \( 21 + 3.5 = 24.5 \, \text{m} \) Area of the park with the path = \( \pi \times (24.5)^2 \) Area of the park without the path = \( \pi \times (21)^2 \) Thus, the area of the path is: \[ \text{Area of path} = \pi \times (24.5)^2 - \pi \times (21)^2 = \pi \times (600.25 - 441) = \pi \times 159.25 = 500.76 \, \text{m}^2 \] The cost of gravelling = \( 500.76 \times 4 = 2003.04 \, \text{Rs.} \) Thus, the cost is approximately Rs. 1802. - Option (A) Rs. 1672: Incorrect. The correct value is higher.
- Option (B) Rs. 1652: Incorrect. This is too low.
- Option (D) Rs. 2048: Incorrect. This exceeds the correct amount.