| ABCDEF is any hexagon with different vertices A, B, C, D, E and F as the centres of circles with same radius r are drawn. The area of the shaded portion is: |
 |
A) \[\pi {{r}^{2}}\]
B) \[2\pi {{r}^{2}}\]
C) \[3\pi {{r}^{2}}\]
D) \[4\pi {{r}^{2}}\]
Correct Answer: B
Solution :
| [b] Internal angles of a regular Hexagon \[=120{}^\circ \] |
| Area of one sector \[=\frac{120{}^\circ }{360{}^\circ }\times \pi \times {{r}^{2}}=\frac{1}{3}\pi {{r}^{2}}\] |
| \[\therefore \]Area of 6 sectors \[=6\times \frac{1}{3}\pi {{r}^{2}}=2\pi {{r}^{2}}\] |
You need to login to perform this action.
You will be redirected in
3 sec
