| ABC is an equilateral triangle. The area of the shaded region if the radius of each of the circle is \[\text{1 cm},\] is: |
 |
A) \[2-\frac{\pi }{3}\]
B) \[\sqrt{3}-\pi \]
C) \[\sqrt{3}-\frac{\pi }{2}\]
D) \[\sqrt{3}-\frac{\pi }{4}\]
Correct Answer: C
Solution :
| [c] Side of triangle \[=2\,cm\] |
| \[\therefore \] Area of triangle \[=\frac{\sqrt{3}}{4}\times {{2}^{2}}=\sqrt{3}\,c{{m}^{2}}\] |
| Area of one sector \[=\frac{60{}^\circ }{360{}^\circ }\times \pi \times {{1}^{2}}=\frac{1}{6}\pi c{{m}^{2}}\] |
| Area of 3 sector \[=3\times \frac{1}{6}\pi =\frac{1}{2}\pi c{{m}^{2}}\] |
| Area of shaded region \[=\left( \sqrt{3}-\frac{\pi }{2} \right)c{{m}^{2}}\] |
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