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Question
A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, find the area of the road.
Solution
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
= `π"r"_2^2 - π"r"_1^2`
= `π["r"_2^2 - "r"_1^2]`
= `22/7 [(126)^2 - (105)^2]`
= `22/7 [126 - 105][126 + 105]`
= `22/7 xx 21 xx 231`
= 22 × 3 × 231
= 66 × 231
= 15246 cm2
∴ Area of road = 15246 cm2
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