Question

what is the area of the shaded sector?
○ $24\pi$
○ $45\pi$
○ $72\pi$
○ $576\pi$
a circle with center o, radius oe = 24, the central angle of the shaded sector doe is $45^\circ$

Explanation:

Step1: Recall sector area formula

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

Step2: Identify given values

$\theta = 45^\circ$, $r = 24$

Step3: Substitute values into formula

$\text{Area} = \frac{45^\circ}{360^\circ} \times \pi \times 24^2$

Step4: Simplify the expression

First, $\frac{45}{360} = \frac{1}{8}$, and $24^2 = 576$. Then $\frac{1}{8} \times 576\pi = 72\pi$

Answer:

72π