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A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, then find the area of the road.

Answer:

Circular road and park are concentric circles.

Radius of the park = r1 = 105 m

Width of road = 21 m

Radius of circular road and park = r2 = 105 m + 21 m = 126 m

So, Area of road = Area of park and road – Area of park

=\pi r_{2}^{2}-\pi r_{1}^{2} \\ =\pi\left[r_{2}^{2}-r_{1}^{2}\right] \\ =\frac{22}{7}\left[(126)^{2}-(105)^{2}\right] \\ =\frac{22}{7}[126-105][126+105] \\ =\frac{22}{7} \times 21 \times 231 \\ =22 \times 3 \times 231=66 \times 231=15246 \mathrm{~m}^{2}

∴ Area
of road = 15246 m^{2}

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