Question

The perimeter of a circular garden is 440m. A path 1.4m runs inside the park. find the cost of gravelling the path at the rate of Rs.100 per square meter.​

Answer 1

Cost = Rs. 6095.95

Explanation:

We are given the perimeter as 440m.

Mow,perimeter of a circle is also called circumference.

Formula for circumference of a circle is;

C = 2πR

Thus:

2πR = 440

R = 440/2π

R = 70 m

We are told that A path 1.4m runs inside the park. Thus radius of smaller circle: r = 70 - 1.4 = 68.6 m

Area of larger circle: A1 = πR² = π(70²)

A1 = 4900π

Area of smaller circle: A2 = πr² = π(68.6²)

A2 = 4705.96π

Area of path = A1 - A2

Area of path = 4900π - 4705.96π

Area of path = 194.04π Sq.m

We want to find the cost of gravelling the path at the rate of Rs.100 per square meter.

Thus;

Cost = 100 × 194.04π

Cost = Rs. 6095.95