ABC26GN4617 · Area

Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:

There are three circles each of radius $\sqrt{7} \mathrm{cm}$. A triangle is formed by joining their centres. The angles at the centre made by the triangle are shown in the figure. The area of the shaded portion is ![](

(a)$\frac{4}{7} \mathrm{cm}^{2}$

(b)$\frac{11}{7} \mathrm{cm}^{2}$

(c)$\frac{22}{7} \mathrm{cm}^{2}$

(d)$11 \mathrm{cm}^{2}$

Answer

Answer (as printed): D

Explanation

Area of the shaded portion $$\begin{aligned} & =\left(\pi r^{2} \times \frac{42}{360}+\pi r^{2} \times \frac{58}{360}+\pi r^{2} \times \frac{80}{360}\right) \mathrm{cm}^{2} \\ = & {\left[\frac{\pi r^{2}}{360}(42+58+80)\right] \mathrm{cm}^{2}=\left[\frac{22}{7} \times(\sqrt{7})^{2} \times \frac{180}{360}\right] \mathrm{cm}^{2}=11 \mathrm{cm}^{2} . } \end{aligned}$$

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