Question

the area of the sector below is (pi).
(60^{circ})(r = 6)

Explanation:

Step1: Recall sector - area formula

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

Step2: Substitute the given values

We are given that $\theta = 60^{\circ}$ and $r = 6$. Substitute these values into the formula:
$A=\frac{60^{\circ}}{360^{\circ}}\times\pi\times(6)^{2}$

Step3: Simplify the expression

First, $\frac{60^{\circ}}{360^{\circ}}=\frac{1}{6}$, and $(6)^{2}=36$. Then $A=\frac{1}{6}\times\pi\times36$.
$A = 6\pi$

Answer:

$6$