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 = $2\mathrm{\pi }R$
$$\begin{gathered} \Rightarrow 396=2\times \frac{22}{7}\times R \\ \Rightarrow R=\frac{396\times 7}{44} \\ \Rightarrow R=63 \end{gathered}$$

Circumference of the inner track = $2\mathrm{\pi }r$
$$\begin{gathered} \Rightarrow 352=2\times \frac{22}{7}\times r \\ \Rightarrow r=\frac{352\times 7}{44} \\ \Rightarrow r=56 \end{gathered}$$

Width of the track = Radius of the outer track $-$ Radius of the inner track
$$\begin{gathered} =63-56 \\ =7\mathrm{m} \end{gathered}$$

Area of the outer circle = $\mathrm{\pi }{R}^2$
$$\begin{gathered} =\frac{22}{7}\times 63\times 63 \\ =12474{\mathrm{m}}^2 \end{gathered}$$

Area of the inner circle = $\mathrm{\pi }{R}^2$
$$\begin{gathered} =\frac{22}{7}\times 56\times 56 \\ =9856{\mathrm{m}}^2 \end{gathered}$$

Area of the track = 12474 $-$ 9856
= 2618 ${\mathrm{m}}^2$