Question

A racetrack is in the form of a ring whose inner circumference is 528 m and the outer circumference is 616 m. Find the width of the track.

Answer 1

Let the inner and outer radii of the track be r metres and R metres, respectively.

Then, $2\mathrm{\pi r}$ = 528
$2\mathrm{\pi R}$ = 616
⇒ $2\times \frac{22}{7}\times r=528$
$2\times \frac{22}{7}\times R=616$
⇒ r = $\left(528\times \frac{7}{44}\right)=84$
R = $\left(616\times \frac{7}{44}\right)=98$
⇒ (R - r) = (98 - 84) m = 14 m
Hence, the width of the track is 14 m.