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.

Answer 1

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.)