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.

Answer 1

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