Question

Question 70

There is a circular pond and a footpath runs along its boundary. A person walks around it, exactly once keeping close to the edge. If his step is 66 cm long and he takes exactly 400 steps to go around the pond, then find the diameter of the pond.

Answer 1

Let the radius of the pond be r. Then, diameter of the pond, $d=2\times r$ [$\because$ diameter = 2 $\times$ radius]
Since a person takes exactly 400 steps with 66 cm long each step to go round the pond.

Hence, the circumference of the pond $=66\times 400$
= 26400 cm
$=\frac{26400}{100}m=264m$
We know that, circumference of a circle is $2\pi r$
$\therefore 2\pi r=264\Rightarrow r=\frac{264}{2}\times \frac{7}{22}=\frac{264\times 7}{44}=42m$
Hence, radius of the pond = 42 m
So, diameter of the pond $=2\times 42=84m$