Question

A race track is in the form of a rig 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 radii of the inner and outer tracks.

Now,

Circumference of the outer track = 2πR

`=> 396 = 2xx22/7xx"R"`

`=> "R" = (396xx7)/44`

⇒ R = 63

Circumference of the inner track = 2πr

`=> 352 = 2xx22/7xx"r"`

`=> r = (352xx7)/44 `

⇒ r = 56

Width of the track = Radius of the outer track -- Radius of the inner track

= 63 - 56

= 7 m

Area of the outer circle = πR²

`=22/7xx56xx56`

= 12474 m²

Area of the inner circle = πR²

`=22/7xx56xx56`

= 9856 m²

Area of the track = 12474 - 9856

                           = 2618 m²