Question

the measure of central angle xyz is $1.25\pi$ radians.
what is the area of the shaded sector?
$10\pi$ units$^2$
$20\pi$ units$^2$
$40\pi$ units$^2$
$80\pi$ units$^2$
the radius of the circle is 8.

Explanation:

Step1: Recall sector area formula

The formula for the area of a sector with central angle $\theta$ (in radians) and radius $r$ is $A = \frac{1}{2}r^2\theta$.

Step2: Identify given values

Radius $r = 8$, central angle $\theta = 1.25\pi$.

Step3: Substitute values into formula

$$\begin{align*} A&=\frac{1}{2} \times 8^2 \times 1.25\pi\\ &=\frac{1}{2} \times 64 \times 1.25\pi \end{align*}$$

Step4: Calculate the numerical product

$\frac{1}{2} \times 64 = 32$; $32 \times 1.25 = 40$, so $A = 40\pi$.

Answer:

$40\pi$ units$^2$