The cost of planting grass in a circular park at the rate of rs4.90/m² is rs24640. A path of uniform width runs around the park. The cost of gravelling the path at the rate of rs3.50/m² is rs3696. Find the cost of fencing the path on both sides at the rate of rs2.10/m
Answers
Answer:
Rs 1108.8
Step-by-step explanation:
The cost of planting grass in a circular park at the rate of Rs 4.90/m2 is Rs 24, 640. A path of uniform width runs around the park. The cost of gravelling the path at the rate of rs 3.50/m2 is Rs 3696. Find the cost of fencing the path on both sides at the rate of Rs 2.10/m
Its a circular field & uniform path around the park
Let say Radius of inner Park = R m
Let say width of Path = X m
Radius of park including Path = R + X m
Area of a Park = \pi \times R^2 m²
Value of \pi = \frac{22}{7}
Area of a Park = (22/7) × R² m²
Cost of Planting Grass = Rs 4.9 /m²
Cost of Planting grass in Park = 4.9 × (22/7) × R² Rs
As cost of planting Grass is given = Rs 24640
=> 4.9 × (22/7) × R² = 24640
=> R² = 246400 / ( 7 × 22)
=> R² = 1600
=> R = 40
Radius of inner Park = 40 m
Area of Path = Area of Outer circle - Area of Inner Circle
=> Area of Path = (22/7) × (40 + X)² - (22/7) × 40²
=> Area of Path = (22/7) × (1600 + X² + 80X - 1600)
=> Area of Path = (22/7) × (X² + 80X)
Cost of Graveling the path = Rs 3.5 /m²
Cost of Graveling The path = 3.5 × (22/7) × (X² + 80X)
= 11 × (X² + 80X)
cost of graveling the path is given = 3696
=> 11 × (X² + 80X) = 3696
=> X² + 80X = 336
=> X² + 80X - 336 = 0
=> X² + 84X - 4X - 336 = 0
=> X (X + 84) - 4(X +84) = 0
=> (X-4)(X+84) = 0
=> X = 4 as X can not be negative
Width Of Path = 4 m
Inner radius = 40 m
Outer Radius = 40 + 4 = 44 m
Inner circumference = 2 × (22/7) × 40 = 44 × 40/7 m
Outer circumference = 2 × (22/7) × 44 = 44 × 44/7 m
As fencing need to be done both side
so total to be fenced = 44 × 40/7 + 44 × 44/7
= 44 × (40 + 44) /7
= 44 × 84/7
= 44 × 12
= 528 m
Cost Of fencing the path = Rs 2.1 m
Total cost of Fencing = 2.1 × 528 = Rs 1108.8