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Question
A circular pond is surrounded by a 2 m wide circular path. If outer circumference of circular path is 44 m, find the inner circumference of the circular path. Also find area of the path.
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Solution
Let R and r be the radius of outer circle and inner circle, respectively.
It is given that, circumference of outer circle is 44 m.
∴ 2πR = 44 ...[∵ Circumference of circle = 2πr]
⇒ `2 xx 22/7 xx R = 44`
⇒ `R = 44/(2 xx 22/7) = (7 xx 44)/(2 xx 22) = 7 m`
Since, r = (R – 2) m = (7 – 2) m = 5 m
∴ Inner circumference of the circular path = 2πr
= `2 xx 22/7 xx 5`
= 31.43 m (approx.)
∵ Area of path = Area of outer circle – Area of inner circle
= π(R2 – r2)
= `22/7 (7^2 - 5^2)`
= `22/7 xx 24`
= 75.43 m2 (approx.)
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