Question

If $\theta$ is in radian, area of the sector = $r^2\theta$

• A. True
• B. False

Answer 1

The correct option is B

False

If $\theta =2\pi$, it will be a full circle and the area will be $\pi r^2$

$\underset{–}{Angle}$ $\underset{–}{Area}$
$2\pi \to \pi r^2$

$1\to \frac{\pi r^2}{2\pi }=\frac{r^2}{2}$

$\theta \to \frac{1}{2}{r}^2\theta$

$Keysteps:$(1) Knowing that $2\pi$ radian corresponds to $\pi r^2$ area
$or$
(2) Knowing the formula sector area = $\frac{1}{2}{r}^2\theta$