Question

There are two circles of different radii such that radius of the smaller circle is three seventh that of the larger circle. A square whose area equals 3969 square cm has its side as thrice the radius of the larger circle. What is the circumference of the smaller circle?

Answer 1

Given that, there are two circles of different radii such that radius of the smaller circle is three seventh that of the larger circle.

Also, a square whose area is $3969c{m}^2$ has its side as thrice the radius of the larger circle.

To find out: The circumference of the smaller circle.

We know that, area of a square $=side\times side$

$\therefore$ Side of the square $=\sqrt{3969}=63cm$

Hence, radius of the larger circle $=63\times \frac{1}{3}$$=21cm$

And radius of smaller circle $=21\times \frac{3}{7}=9cm$

We know that, the circumference of a circle is $2\pi r$

$\therefore$ The circumference of the smaller circle $=2\times \frac{22}{7}\times 9[\because \pi =\frac{22}{7}]$

$\Rightarrow 56.5714cm$

Hence, the circumference of the smaller circle is $56.5714cm$.