Question

Question 110

A circular pond is surrounded by a 2m wide circular path. If the outer circumference of circular path is 44 m, find the inner circumference of the circular path. Also, find the 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.
$\therefore$ $2\pi R=44$ $[\because$ circumference of circle = $2\pi r$]
$\Rightarrow 2\times \frac{22}{7}\times R=44$
$\Rightarrow R=\frac{44}{2\times \frac{22}{7}}=\frac{7\times 44}{2\times 22}=7m$
Since, r = (R- 2) m = (7-2) m = 5 m
$\therefore$ Inner circumference of the circular path $=2\pi r=2\times \frac{22}{7}\times 5=31.43\text{m(approx)}$.
$\because$ Area of path = Area of outer circle - Area of inner circle $=\pi (R^2-r^2)$
$=\frac{22}{7}(7^2-5^2)=\frac{22}{7}\times 24=75.43m^2\text{(approx.)}$