Question

the area of a sector of the circle with an arc measure of 30° and with a radius of 6 is ____. 30° 6 o 3π 3 9π 12π

Explanation:

Step1: Recall sector area formula

The formula for the area of a sector is $A = \frac{\theta}{360^\circ} \times \pi r^2$, where $\theta$ is the central angle in degrees, and $r$ is the radius.

Step2: Substitute given values

$\theta = 30^\circ$, $r = 6$. Substitute into the formula:
$A = \frac{30^\circ}{360^\circ} \times \pi \times 6^2$

Step3: Simplify the expression

First, simplify $\frac{30}{360} = \frac{1}{12}$, and $6^2 = 36$.
$A = \frac{1}{12} \times \pi \times 36 = 3\pi$

Answer:

3π