Question

The inner circumference of a circular race track is $44m$ less than the outer circumference. If the outer circumference is $396m$, then find the width of the track.

Answer 1

Outer circumference $=396m$

Inner circumference $=(396-44)m=352m$

Let outer radius be $R$ and inner radius be $r$.

$\therefore 2\pi R=396$

$\Rightarrow 2\times \frac{22}{7}\times R=396$

$\Rightarrow R=\frac{396\times 7}{2\times 22}$

$\Rightarrow R=63$

and,

$2\pi r=352$

$\Rightarrow 2\times \frac{22}{7}\times r=352$

$\Rightarrow r=\frac{352\times 7}{2\times 22}$

$\Rightarrow r=56$

Therefore, width of track = $(63-56)m=7$ $m$.