Question

For a given square, if the area of its incircle is $100 𝑐𝑚^2$ , then the area of its circumcircle is __________ $𝑐𝑚^2$ (rounded off to the nearest integer).

Answer 1

Correct Answer: 200

The radius of the incircle is given by:

\( r = \sqrt{\frac{\text{Area of incircle}}{\pi}} = \sqrt{\frac{100}{\pi}}. \)

The radius of the circumcircle is \(\sqrt{2}\) times the radius of the incircle:

\( R = \sqrt{2} \cdot r = \sqrt{2} \cdot \sqrt{\frac{100}{\pi}}. \)

The area of the circumcircle is:

\( \text{Area} = \pi R^2 = \pi \left( \sqrt{2} \cdot \sqrt{\frac{100}{\pi}} \right)^2 = 200 \text{ cm}^2. \)