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Question
The outer circumference of a circular race-track is 528 m . The track is everywhere 14 m wide. Calculate the cost of levelling the track at the rate of 50 paise per square metre.
`(use pi=22/7). `
Solution
Let the radius of the inner circle and the race track be R m.
Outer circumference of the race track = 528 m
`⇒ 2 pi R=528`
`⇒ R=528/2pi=84 m`
Total radius of the outer circle =` 84-14=70 m`
Area of the circular track = Area of the outer circle − area of inner circle
`= pi(84)^2-pi(70)^2`
`= pi [(84-70)(84+70)]`
`=pi(14)(154)`
`=6776 m^2`
Cost of levelling the track =` 0.5xx6776=Rs 3388`
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