Bunuel wrote:

The area of the circumscribed circle in the figure above is 32. What is the area of the square?

A. \(\frac{8}{\pi}\)

B. \(\frac{8\sqrt{2}}{\pi}\)

C. \(\frac{32}{\pi}\)

D. \(\frac{64}{\pi}\)

E. 32

Attachment:

image001 (1).jpg

Formula used to calculate the area of circumscribed square \(2*r^2\) where r is radius of circle

Dagonal of square is equal to diameter of circle Area of Circle \(\pi*r^2\) =\(32\)

Taking square root on both sides

\(\sqrt{\pi*r^2}\) = \(\sqrt{32}\)

i.e \({\sqrt{\pi}}*r\)= \(\sqrt{16*2}\)

i.e \({\sqrt{\pi}}*r\)= \(4\sqrt{2}\)

so r = \(\frac{4\sqrt{2}}{\sqrt{\pi}}\)

2 * \(\frac{4\sqrt{2}}{\sqrt{\pi}}\) * \(\frac{4\sqrt{2}}{\sqrt{\pi}}\) = \(\frac{2 *32}{\pi}\) = \(\frac{64}{\pi}\)

Bunuel pushpitkc can you pls format my explanation - (the square roots/ radicals/ fractions in a math friendly way

thank you