Question

Diameter of the circular garden is 42 m. There is a 3.5 m wide road around the garden. Find the area of the road.

Answer 1

Diameter of the garden(d) = 42 m
Radius, r = 21 m
Diameter of the garden including the road = 42 + 3.5 + 3.5 = 49 m
Radius of the garden with the road = 24.5 m
Area of road =
$$\begin{gathered} \mathrm{Ar}\mathrm{of}\mathrm{garden}\mathrm{with}\mathrm{road}-\mathrm{Ar}\mathrm{of}\mathrm{garden} \\ =\mathrm{\pi }{R}^2-\mathrm{\pi }{r}^2 \\ =\mathrm{\pi }\left(R^2-r^2\right) \\ =\frac{22}{7}\left({\left(24.5\right)}^2-{21}^2\right) \\ =\frac{22}{7}\times \left(600.25-441\right) \\ =\frac{22}{7}\times 159.25 \\ =500.5{\mathrm{m}}^2 \end{gathered}$$