Question

a school ground is in the shape of a circle with radius 103 m. four tracks each of 3 m wide has to be constructed inside the ground for the purpose of track events. find the cost of constructing the track at the rate of rs. 50 per sq.m.

Answer 1

To find the cost of constructing the track, we need to calculate the area of the track and then multiply it by the rate of construction. The area of the track is given by the formula A = π(R^2 - r^2). Substituting the values, the area is 1965.78 sq.m. The cost of constructing the track is Rs. 98289.

Step-by-step explanation:

To find the cost of constructing the track, we need to calculate the area of the track and then multiply it by the rate of construction.

The track consists of four segments, each with a width of 3 m. So, the inner radius of the track will be the radius of the school ground minus 3 m.

The area of the track is given by the formula A = π(R^2 - r^2), where R is the outer radius of the track and r is the inner radius.

Substituting the values, A = π((103+3)^2 - 103^2) = π(106^2 - 103^2) = 3.14(11236 - 10609) = 3.14(627) = 1965.78 sq.m.

The cost of constructing the track is found by multiplying the area by the rate of construction, so the cost = 1965.78 sq.m. * Rs.50/sq.m. = Rs. 98289.