Statement A (Assertion) : In the given figure, if arcs are drawn … - Vidyadip

MCQ

Statement A (Assertion) : In the given figure, if arcs are drawn by taking vertices $A$, $B$ and $C$ of an equilateral triangle of side $8 cm$, to intersect the sides $B C, C A$ and $A B$ at their respective mid-points $D, E$ and $F$, then area of the shaded region is $25.12 cm ^2$. (Use $\pi=3.14$ )

Statement R (Reason) : The area of a sector of a circle of radius $r$ with sector angle $\theta$ is $\frac{\theta}{180^{\circ}} \times \pi r^2$ sq. units.

A
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
✓
Assertion $(A)$ is true but reason $(R)$ is false.
D
Assertion (A) is false but reason $(R)$ is true.

✓

Answer

Correct option: C.

Assertion $(A)$ is true but reason $(R)$ is false.

(c) : Given, $\triangle A B C$ is an equilateral triangle.
$\therefore \angle A=\angle B=\angle C=60^{\circ}$ and radius, $r=\frac{8}{2} cm =4 cm$
Area of sector AFEA $=\frac{\theta}{360^{\circ}} \times \pi r^2=\frac{60^{\circ}}{360^{\circ}} \times \pi(4)^2$
$
=\frac{8}{3} \pi cm ^2
$Since, area of all three sectors are equal.
$\therefore \quad$ Total area of shaded region $=3\left(\frac{8}{3} \pi\right)=25.12 cm ^2$
So, assertion and reason both are true but reason is not the correct explanation of assertion.

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