A circular park has a path of uniform width around it. The difference between the outer and inner circumferences of the circular path is 132 m. Its width is
(a) 20 m
(b) 21 m
(c) 22 m
(d) 24 m
Let OA = r be the radius of the inner circle and OB = r′ be the radius of the outer circle.
Therefore, circumference of the inner circle $=2 \pi r$ and circumference of the outer circle $=2 \pi r^{\prime}$
Here we have to find the width of the circular park that is we have to find $r^{\prime}-r$.
We have given the difference between the circumferences of outer circle and inner circle.
$\therefore 2 \pi r^{\prime}-2 \pi r=132$
$\therefore 2 \pi\left(r^{\prime}-r\right)=132$
Substituting $\pi=\frac{22}{7}$ we get,
$2 \times \frac{22}{7} \times\left(r^{\prime}-r\right)=132$
Now we will multiply both sides of the equation by $\frac{7}{44}$.
$\left(r^{\prime}-r\right)=132 \times \frac{7}{44}$
$\therefore\left(r^{\prime}-r\right)=3 \times 7$
$\therefore\left(r^{\prime}-r\right)=21$
Therefore, the width is $21 \mathrm{~m}$.
Hence the correct answer is option (b).