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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?

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Solution

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 3969 cm2 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×side
Side of the square =3969=63 cm

Hence, radius of the larger circle =63×13=21 cm

And radius of smaller circle =21×37=9 cm

We know that, the circumference of a circle is 2πr
The circumference of the smaller circle =2×227×9[ π=227]
56.5714 cm

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

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