Question

The outer circumference of a circular race-track is $528m$ . The track is everywhere $14m$ wide. Calculate the cost of levelling the track at the rate of $50$ paise per square metre . Use $\pi =\frac{22}{7}$

Answer 1

Let the radius of the outer circle be $Rm$.

Outer circumference of the race track $=528m$

$\Rightarrow 2\pi R=528\Rightarrow R=5282\pi \Rightarrow R=5282\times \frac{22}{7}=84m$

$\therefore$ radius of the inner circle $r=84-14=70m$

Area of the circular track = Area of the outer circle − area of inner circle
$=\pi {84}^2-\pi {70}^2=\pi ({84}^2-{70}^2)=\frac{22}{7}\times 2156=6776m^2$

$\therefore$ Cost of levelling the track $=0.5\times 6776=Rs.3388$
Hence, the cost of levelling the track is $Rs.3388$