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

A. 1.967 cm²

B. 1.975 cm²

C. 19.67 cm²

D. 21.21 cm²

Answer: Option A

Solution(By Examveda Team)

Required area = (Area of an equilateral Δ of side 7 cm) - (3 × Area of sector with θ = 60° and r = 3.5 cm)
$$ = \left[ {\left( {\frac{{\sqrt 3 }}{4} \times 7 \times 7} \right) - \left( {3 \times \frac{{22}}{7} \times 3.5 \times 3.5 \times \frac{{60}}{{360}}} \right)} \right]c{m^2}$$
$$\eqalign{ & = \left( {\frac{{49\sqrt 3 }}{4} - 11 \times 0.5 \times 3.5} \right)c{m^2} \cr & = (21.217 - 19.25)c{m^2} \cr & = 1.967\,c{m^2} \cr} $$