ABC26GN4659 · Area
Subject: General Aptitude · Chapter: Area · Exam: 2003 · Marks: · Difficulty:
Three circles 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)$1.967 \mathrm{cm}^{2}$
(b)$1.975 \mathrm{cm}^{2}$
(c)$19.67 \mathrm{cm}^{2}$
(d)$21.21 \mathrm{cm}^{2}$
Answer
Explanation
Required area $=($ Area of an equilateral $\Delta$ of side 7 cm$)-(3 \times$ area of sector with $\theta=60^{\circ}$ and $r=3.5 \mathrm{cm}$ ) $$\begin{aligned} & =\left[\left(\frac{\sqrt{3}}{4} \times 7 \times 7\right)-\left(3 \times \frac{22}{7} \times 3.5 \times 3.5 \times \frac{60}{360}\right)\right] \mathrm{cm}^{2} . \\ & =\left(\frac{49 \sqrt{3}}{4}-11 \times 0.5 \times 3.5\right) \mathrm{cm}^{2} \\ & =(21.217-19.25) \mathrm{cm}^{2}=1.967 \mathrm{cm}^{2} . \end{aligned}$$
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