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
Hi!
Here is the answer to your query.
Let the radius of the circular park be r m.
Area of the circular park = πr2
Cost of planting grass in 1 m2 = Rs 4.90
∴Rs 4.90 × πr2 = Rs 24640
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Let the width of the path be x m.
Area of the path = π [(40 + x)2 – (40)2]
∴ Rs 3.50 × π [(40 + x)2 – (40)2 ] = Rs 3696
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⇒ x2 + 80x – 336 = 0
⇒ x2 + 84x – 4x – 336 = 0
⇒ x (x + 84) – 4(x + 84) = 0
⇒(x + 84)( x –4)= 0
⇒ x + 84 = 0 or x –4 = 0
⇒ x = – 84 or x = 4
⇒ x = 4
Width of the park = 4 m
Length of the wire needed to fence the path on both sides = Circumference of the inner circle + Circumference of outer circle
Circumference of the inner circle = 2π × 40 cm = 80π m
Circumference of outer circle = 2π × 44 cm = 88π m
Length of the wire needed to fence the path on both sides = (80π+ 88π) m = 168π m.
Cost of fencing 1 m = Rs 2.10
∴Cost of fencing 168π m = Rs 2.10 × 168π = Rs 1108.80
Thus, the cost of fencing the path on both sides is Rs 1108.80.
Cheers!