Question

A circular running track is such that the outer radius of the track is 21 m and the inside radius is 14 m. Synthetic mat is to be laid on the running track. If the cost of laying the synthetic mat at the rate of Rs. 1000 per $m^2$ is X. Find X

Answer 1

The synthetic mat is to be laid on the circular track. The outer radius of the track is 21 m and the internal radius of the track is 14 m.

So we can assume that the area required to lay the synthetic track is = The area of the outer circle – the area of the internal circle

Let us consider the radius of the outer circle is ‘R’ = 21 m

Then, The area of the outer circle = $\pi R^2$ = $\frac{22}{7}\times {21}^2$ = 1386 $m^2$

Now, let us consider the radius of the internal circle is ‘r’ = 14 m

Then, the area of the internal circle = $\pi r^2$ =$\frac{22}{7}\times {14}^2$ = 616$m^2$

The area of the track is = Area of the outer circle – Area of the internal circle = 1386 – 616 = 770 $m^2$

Now that we know the area required for laying the synthetic mat we will try to find the cost of laying the mat. The cost of laying the track is Rs 1000 per $m^2$.

Therefore the total cost = Cost of laying the $\frac{mat}{m^2}$ x Total area for laying the mat = 1000 x 770 = Rs 7,70,000