Question

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

Answer 1

$\Rightarrow$ Circumference of a outer circular track $=2\pi R$

$\therefore$ $528=2\times \frac{22}{7}\times R$

$\therefore$ $R=\frac{528\times 7}{44}=84m$

$\Rightarrow$ As the circular park is $14m$ wide.

$\Rightarrow$ Then inner radius $r=84m-14m=70m$

$\Rightarrow$ Area of the circular track = Area of outer circle - Area of the inner circle.

$\Rightarrow$ Area of the circular track $=\pi R^2-\pi r^2$

$\Rightarrow$ Area of the circular track $=\frac{22}{7}\times (84{)}^2-\frac{22}{7}\times (70{)}^2=\frac{22}{7}({84}^2-{70}^2)$

$\Rightarrow$ Area of the circular track $=\frac{22}{7}(84-70)(84+70)=\frac{22}{7}\times 14\times 154$

$\therefore$ Area of the circular track $=6776m^2$

$\Rightarrow$ Cost of levelling the track $50paise/m^2$

$\therefore$ Total cost $=6776\times 0.50=Rs.3388$