Question

A regular hexagon is drawn with its vertices on a circle as shown in the figure. Without looking into it, if one randomly puts a dot in it, what is the probability of the dot not being in the regular hexagon?

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

Answer 1

The correct option is C

$\frac{3\sqrt{3}}{2\pi }$

Area of the circle = $\pi \times r^2$

Area of regular hexagon = $\frac{\sqrt{3}{r}^2}{4}\times 6$ =$\frac{3\sqrt{3}{r}^2}{2}$

Required probablity = $\frac{\frac{3\sqrt{3}{r}^2}{2}}{\pi r^2}$ = $\frac{3\sqrt{3}{r}^2}{2}\times \frac{1}{\pi r^2}$

= $\frac{3\sqrt{3}}{2\pi }$