A circular park of radius 20m has a road 5m wide running around it.Find the cost of metalling the road at rupees 14 per square m

Answer :

We have a circular park , with radius OA =  20 m
and
5 m wide road around that park ,
So,
Radius of outer circle =  OB  = OA  + AB  = 20 + 5  =  25 m

We know

Area of Circle  = $\pi r^2$
So
Area of road  = area of outer circle - area of inner circle 

$$\begin{gathered} \mathrm{area} \mathrm{of} \mathrm{road} = \mathrm{\pi }\left({\mathrm{OB}}^2 - {\mathrm{OA}}^2\right) \\ \Rightarrow \mathrm{Area} \mathrm{of} \mathrm{road} = \mathrm{\pi }\left[{\left(25\right)}^2 - {\left(20\right)}^2\right] \\ \Rightarrow \mathrm{Area} \mathrm{of} \mathrm{road} = \frac{22}{7}\left(625-400\right) = \frac{4950}{7}{\mathrm{m}}^2 \\ \mathrm{cost} \mathrm{of} \mathrm{metalling} 1 {\mathrm{m}}^2 \mathrm{of} \mathrm{road} = \mathrm{Rs} 14 \\ \mathrm{cost} \mathrm{of} \mathrm{metalling} \frac{4950}{7}{\mathrm{m}}^2 \mathrm{of} \mathrm{road} = \mathrm{Rs}\left(\frac{4950}{7}\times 14\right) = \mathrm{Rs} 9900 \end{gathered}$$