Question

The circumference of a circular garden is 88 m. It is surrounded by a path of uniform width 3.5 m. Find the cost of gravelling the path at the rate of Rs. 20/m

Answer 1

Answer:-

Given:

Circumference of a circular garden = 88 m

Width of the path around the garden = 3.5 m

We know that,

Circumference of a circle = 2πr

Hence,

2πr = 88

→ 2 * 22/7 * r = 88

→ r * 44/7 = 88

→ r = 88 * 7/44

→ r = 14

→ Radius of the garden = 14 m

Now,

Perimeter of the path = Perimeter of garden along with the path - Perimeter of the garden.

Hence,

Perimeter of garden along with the path = 2π * (14 + 3.5)

→ Perimeter of the garden along with path = 2 * π *(17.5)

→ Perimeter of the garden along with path = 2 * 22/7 * 175/10

→ Perimeter of the garden along with path = 110 m

We have,

Perimeter of the garden = 88 m

Hence,

→ Perimeter of the path = 110 - 88

→ Perimeter of the path = 22 m

Cost of gravelling the path = Rs 20 per m.

Total Cost of gravelling the path = 20 * Perimeter of the path

→ Cost of gravelling the path = 20 * 22

→ Cost of gravelling the path = Rs. 440

Answer 2

Step-by-step explanation:

Circumference of ground =88 m

⇒2πr=88

⇒r=14 m ....take π= 22/7

Area of strip to be levelled = Area of ground − Area of inner circle

=π14

2

−π11

2

=235.72 m

....take π= 22/7

Total cost of levelling the strip (if the cost of levelling 1 m is Rs. 7) =235.72×7

= Rs. 1650