Question

If three equal circles of radius $3$ cm each touch each other, then the area of the shaded portion is

• A. $\frac{\sqrt{3}}{2}(2-\pi ){\text{cm}}^2$
• B. $\frac{9}{2}(2\sqrt{3}-\pi ){\text{cm}}^2$
• C. $\frac{9}{2}(2\sqrt{3}+\pi ){\text{cm}}^2$
• D. $\frac{3}{2}(\sqrt{3}-\pi ){\text{cm}}^2$

Answer 1

The correct option is B $\frac{9}{2}(2\sqrt{3}-\pi ){\text{cm}}^2$

Area of the equilateral trianble (formed by joining the centres) of side 6 cm- Area of three equal sectors of central angle${60}^0$
$=\frac{\sqrt{3}}{4}\times 6^2-3\times \frac{60}{360}\times \pi {.3}^2$
$=\frac{9}{4}\sqrt{3}-\frac{9}{2}\pi =\frac{9}{2}(2\sqrt{3}-\pi )$