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Question
A racetrack is in the form of a ring whose inner circumference is 352 m and outer circumference is 396 m. Find the width and the area of the track.
Solution
Let r m and R m be the inner and outer boundaries, respectively.
Thus, we have:
2πr = 352
`⇒ r = 352/(2pi)`
Also,
2πR = 396
⇒ 2πR = 396
`⇒ "R" = 396/(2pi)`
Width of the track = (R - r)
`=((396)/(2pi) -(352)/(2pi) )`
`= 1/(2pi)(396-352) "m"`
`=(1/2xx7/22xx44) "m"`
= 7 m
Area of the track =π (R2 - r2)
= [π (R + r) (R - r)
`= [pi(396/(2pi) + (352)/(2pi))xx((396)/(2pi)-(352)/(2pi))]"m"^2`
`=(pixx748/(2pi)xx7)"m"^2`
`=748/2xx7"m"^2`
= 2618 m2
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