Question

The cost of planting the grass in a circular park @ Rs. 5 per m2 is Rs. 27720. A path of uniform width runs around the park. The cost of gravelling the path @ Rs. 3.50 per m2. Is Rs. 10780. Find the cost of fencing the path on both sides @ Rs. 2.1 per m.

Answer 1

Let the radius of inner circle be 'r' and radius of outer circle be 'R'

Cost of planting grass in the park:

Rs 5 for 1 m² area
Rs 1 for 1/5 m² area
Rs 27720 for 27720 X 1/5 = 5544 m² area
Area of the park is 5544 m²
π r² = 5544 [ Area of a circle = π r²]
22/7 x r² = 5544
r² = 5544 x 7/22
r² = 1764
r = √1764 = 42m

Cost of gravelling the path
Rs 3.50 for 1 m²
Rs 1 for 1/3.50 m²
Rs 10780 for 10780 X 1/3.50 = 3080 m²
Area of path = 3080 m²
Area of Path = Area of outer boundary minus area of inner boundary
Area of path = π R² - π r²
= π (R² - r²)
3080 = π (R² - r²)
3080 = 22/7 (R² - 1764)
3080 x 7/22 = R² - 1764
980 = R²- 1764
R² = 2744
R = √2744 = 52.38 m
cost of fencing = (circumference of outer circle - circumference of inner circle) x rate per m.
(2πR - 2πr) x 3
2π (52.38 - 42) X 3
= 2 X 22/7 X 10.38 X 3 = Rs 195.74

Hope it helps u