Question

If the area of a circle is $A_1$ and the area of the regular hexagon inscribed in the circle is $A_2,$ then the value of $\frac{A_1}{A_2}$ is

• A. $\frac{\pi }{3\sqrt{3}}$
• B. $\frac{2\pi }{3\sqrt{3}}$
• C. $\frac{4\pi }{3\sqrt{3}}$
• D. $\frac{8\pi }{3\sqrt{3}}$

Answer 1

The correct option is B $\frac{2\pi }{3\sqrt{3}}$

Let the radius of the circle be $R.$
$A_1=\pi R^2$

$A_2=6\times \frac{1}{2}\times R^2\sin {60}^{\circ }=\frac{3\sqrt{3}}{2}{R}^2\therefore \frac{A_1}{A_2}=\frac{2\pi }{3\sqrt{3}}$