Question

In the figure above, the smaller circle is inscribed in the square and the square is inscribed in the larger circle. If the length of each side of the square is s, which is the ratio of the area of the larger circle to the area of the smaller circle?

• A. $2\sqrt{2}:1$
• B. $2:1$
• C. $\sqrt{2}:1$
• D. $2s:1$
• E. $s\sqrt{2}:1$

Answer 1

The correct option is B $2:1$

Side of square =s

For smaller circle raidus r=$\frac{s}{2}$

Digonal of square=$\sqrt{2}s$

For bigger circle Radiu R=$\frac{\sqrt{2}s}{2}$

Ratio of Area=

$\frac{\pi .R^2}{\pi .r^2}\to =\frac{\frac{2s^2}{4}}{\frac{s^2}{4}}$

$\to \frac{2}{1}$