Question

If the angle subtended by the arc of a sector at the center is $90$ degrees, then the area of the sector in square units is

• A. $2\pi r^2$
• B. $4\pi r^2$
• C. $\frac{\pi r^2}{4}$
• D. $\frac{\pi r^2}{2}$

Answer 1

Answer: (C)

$\frac{\pi r^2}{4}$

Since the Central angle is ${90}^{\circ }$, it means it is a Quad-circle.

So the Area of this sector is $\frac{1}{4}$ th of the Circle's Area $=\frac{1}{4}\ast \pi r^2$