Question

convert the angle in degrees to radians by multiplying it to $\frac{pi}{180^{circ}}$. find the area of the sector in the figure. complete each line in the solution by moving one answer to each box. $a=\frac{1}{2}(quad)^2(quad)$ $a = (quad)\text{ in.}^2$

Explanation:

Step1: Convert angle to radians

$30^{\circ}\times\frac{\pi}{180^{\circ}}=\frac{\pi}{6}$ radians

Step2: Recall sector - area formula

The formula for the area of a sector of a circle is $A = \frac{1}{2}r^{2}\theta$, where $r$ is the radius and $\theta$ is the central - angle in radians. Here, $r = 12$ inches and $\theta=\frac{\pi}{6}$.

Step3: Substitute values into formula

$A=\frac{1}{2}(12)^{2}(\frac{\pi}{6})$
$A=\frac{1}{2}\times144\times\frac{\pi}{6}$
$A = 12\pi$

Answer:

$A=\frac{1}{2}(12)^{2}(\frac{\pi}{6})$; $A = 12\pi$ in.$^{2}$