Question

If ${\theta }^{\circ }$ is the angle between two radii of a circle of radius $r,$ then the area of corresponding sector is

• A. $r^2\theta$
• B. $\frac{1}{2}{r}^2\theta$
• C. $r\theta$
• D. $2\pi r$

Answer 1

The correct option is B $\frac{1}{2}{r}^2\theta$

The area of the sector (shaded region) $=$ Area of the circle $\times \frac{\theta }{{360}^0}$

$={\pi r}^2\times \frac{\theta }{2\pi }$

$=\frac{r^2\theta }{2}$ (where $\theta$ should be in radians)