Question

There is a circular pond and foot-path runs along its boundary. A man walks around it, exactly once, keeping close to the edge. If his step is $55$ cm long and he takes exactly $400$ steps to go round the pond. What is the diameter of the pond?

Answer 1

Let the radius of the pond be 'r'. since man takes exactly 400 step of 55 cm to go around the pond.

Hence, the circumference of the pond =$55\times 400$

$=22,000cm$

$=\frac{22000}{100}$

$=220m.$

circumference of the pond is $220m.$

circumference of the circular pond $=2\pi r$

$220=2\pi r$

$\Rightarrow 220=2\times \frac{22}{7}\times r$

$\Rightarrow r=220\times \frac{7}{44}$

$\Rightarrow r=35m$

$\therefore$ Diameter of the pond $=2\times r$

$=2\times 35$

$=70m.$