question_answer

Three circles of radius 3.5 cm each are placed in such a way that each touches the other two. The area of the portion enclosed by the circles is

A)  \[1.975\,\,\text{c}{{\text{m}}^{\text{2}}}\]

B)  \[1.967\,\,\text{c}{{\text{m}}^{\text{2}}}\]

C)  \[19.76\,\,\text{c}{{\text{m}}^{\text{2}}}\]

D)  \[21.21\,\,\text{c}{{\text{m}}^{\text{2}}}\]  

Correct Answer: B

Solution :

Radius of each circle = 3.5 cm

From the figure,

\[\Delta ABC\]will be an equilateral triangle of side 7 cm each.

Now, the required area = Area of \[\Delta ABC-3\times \](Area of a sector of angle \[60{}^\circ \] in a circle of radius 3.5 cm)\[=\frac{\sqrt{3}}{4}\times {{(7)}^{2}}-3\left[ \frac{60}{360}\times \frac{22}{7}{{(3.5)}^{2}} \right]\text{c}{{\text{m}}^{\text{2}}}\]

\[=\left[ \frac{49\sqrt{3}}{4}-19.25 \right]\text{c}{{\text{m}}^{\text{2}}}\]