Question

A school ground is in the shape of a circle with radius 103 m . Four tracks each f 3 m wide has to be constructed inside the ground for the purported purpose of track events. Find the cst of constructing the track at the rate of ₹50 per square metre

Answer 1

For diagram, refer to the hand-drawn image.

Radius of school ground = OA = 103m

∴ area of school ground = πr^2

= 22/7 × (103)^2 square ms...(i)

Now,

Breadth of 1 race track = 3m

∴ breadth of 4 race tracks = 12m

So,

the radius of the remaining area = 103-12 m = 91m

Then, area of the remaining area = πr^2

= 22/7 × (91)^2 square ms...(ii)

Hence, area of the race track = (area of school ground) - (area of remaining area) square ms

= (22/7 × 103 × 103) - (22/7 × 91 × 91) square ms

= 22/7 (103 × 103 - 91 × 91) square ms

= 22/7 (10609 - 8281) square ms

= 22/7 × 2328 square ms

= 51216/7 square ms

= 7316.5 square ms

Now, cost of constructing 1 square metre of track = Rs 50

∴ Cost of constructing 7316.5m of track = Rs 7316.5 × 50

= Rs 73165/10 × 50

= Rs 73165 × 5

= Rs 365825

Ans) The cost of constructing the race track will be Rs 365825