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 event. find the cost of constructing the track at the rate of rupees 50 per sq.m.
Answers
For the 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
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