Question

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/m2is Rs 3696.

1) Find the cost of fencing the path on both sides at the rate of Rs 2.10/m.

soon please

Answer 1

⭕️Let radius of the circular park be r m.

⭕️Area of circular park = πr2

⭕️Cost of planting grass in 1 m2 = Rs 4.90

∴Rs 4.90 x πr2 = Rs 24640

r^2= 24640 x 7 ÷ 4.90 x 22

simplifying;

r= 40

⭕️So the radius of park will be 40m

⭕️ width of the path be x m.

⭕️Area of the path = π [(40 + x)2 – (40)2]

∴ 3.50 × π [(40 + x)2 – (40)2 ] = 3696
simplifying;

⇒ 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 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 = ₹2.10

∴Cost of fencing 168π m = Rs 2.10 × 168π = ₹ 1108.80

✔️✔️the cost of fencing the path on both sides is /= 1108.80



$\huge\bf{\red{\mathfrak{thank \: you :)}}}$

Answer 2

Heyy mate ❤✌✌❤

Here's your Answer....

⤵️⤵️⤵️⤵️⤵️⤵️⤵️

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

=> r^2 = 24640 × 7/ 4.90 × 22

=> r^2 = 1600

=> r = 40m.

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

=> 1600 + 80x + x^2 -1600 = 3696 × 7/ 22 × 3.50. = 336

=>  x^2 + 80x – 336 = 0

⇒ x^2 + 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

Now,

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.

Now,

Cost of fencing 1 m = Rs 2.10

∴Cost of fencing 168π m = Rs 2.10 × 168π = Rs 1108.80
✔✔✔