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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 ₹ 50 per sq.m
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Solution
Radius of the ground R = 103 m
Width of a track W = 3 m
Width of 4 tracks = 4 × 3 = 12 m
Radius of the ground without track
r = (103 – 12) m
r = 91 m
Area of 4 tracks = Area of the ground – Area of the ground without track
= πR2 – πr2 sq.units
= π(R2 – r2) sq.units
= `22/7 [103^2 - 91^2]`
= `22/7 [103 + 91] [103- 91] "m"^2`
= `22/7 xx 194 xx 12`
= `51216/7`
= 7316.57 m2
∴ Area of 4 tracks = 7316.57 m2
Cost of constructing 7316.57 m2 = ₹ 50
∴ Cost of constructing 7316.57 m2 = ₹ 50 × 7316.57
= ₹ 3,65,828,57
Cost of constructing the track ₹ 3,65,828,57
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