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 and R be the radii of inner circle and outer boundaries respectively.

Then,

Circumference of inner circle = 2πr = 352 and

Circumference of outer circle = 2πR = 396

r = 352/2π and R = 396/2π

Width of the track = (R – r) = 396/2π – 352/2π

= 44/2π

= 44/2 x 7/22

= 7

Width of the track is 7 m.

Again, R + r = 396/2π + 352/2π = 748/2π

Area of the track = π(R² – r²)

= π(R – r) (R+r)

= π x 7 x 748/2π

= 2618

Therefore, the area of the track is 2618 m².