Question

The inner circumference of a circular track is 330 m. The track is 10.5 m wide everywhere. Calculate the cost of putting up a fence along the outer circle at the rate of Rs 20 per metre.

Answer 1

Let the inner and outer radii of the track be r metres and (r + 10.5) metres, respectively.

Inner circumference = 330 m
∴ $2\mathrm{\pi r}=330$ ⇒ $2\times \frac{22}{7}\times r=330$
⇒ r = $\left(330\times \frac{7}{44}\right)=52.5\mathrm{m}$
Inner radius of the track = 52.5 m
∴ Outer radii of the track = (52.5 + 10.5) m = 63 m


∴ Circumference of the outer circle = $\left(2\times \frac{22}{7}\times 63\right)\mathrm{m}=396\mathrm{m}$
Rate of fencing = Rs. 20 per metre
∴ Total cost of fencing the outer circle = Rs. (396 $\times$ 20) = Rs. 7920