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Question
A 7 m broad pathway goes around a circular park with a circumference of 352 m. Find the area of road.
Solution
The circumference of the circular park = 352 m.
Let r be the radius of the circular park.
Then, 2πr = 352
`2 xx 22/7 xx r` = 352
r = `(352 xx 7)/(2 xx 22)` = 56 m
Area of circular park = πr2
= `22/7 xx (56)^2`
= `22/7 xx 56 xx 56`
= 22 × 8 × 56
= 9856 m2
Now, the circular park's radius with road,
R = 56 + 7 = 63 m
∴ Circular park area with a road
= πR2
= `22/7 xx (63)^2`
= `22/7 xx 63 xx 63`
= 22 × 9 × 63
= 12474 m2
So, Area of road = Area of circular park with road – Area of circular park
= 12474 – 9856
= 2618 m2
Hence, the area of road is 2618 m2.
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