Question

A road which is 7 m wide surrounds a circular park whose circumference is 352 m. Find the area of of road.

Answer 1

We have :
Circumference of the circular park = 2πr = 352 m
​ ⇒ 2 x $\frac{22}{7}$ x r = 352
⇒ r = 56 m.
Radius of the path including the 7m wide road = (r +7) = 56 +7 = 63 m.
∴ Area of the road :
$$\begin{gathered} =\left[\mathrm{\pi }{\left(63\right)}^2-\mathrm{\pi }{\left(56\right)}^2\right]m^2 \\ =\mathrm{\pi }\left[{\left(63\right)}^2-{\left(56\right)}^2\right]m^2 \\ =\mathrm{\pi }\left[\left(63+56\right)\left(63-56\right)\right]{\mathrm{m}}^2 \\ =\mathrm{\pi }\left[\left(119\right)\left(7\right)\right] \\ =\left(\frac{22}{7}\times 119\times 7\right){\mathrm{m}}^2=\left(22\times 119\right){\mathrm{m}}^2=2618{\mathrm{m}}^2. \end{gathered}$$