Question

select the correct answer. circle o has radius of 24 units. arc xy located on the circle has a central angle of 75°. what is the area of the associated sector, in square units? a. 10π b. 120π c. 5π d. 51π

Explanation:

Step1: Recall sector area formula

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

Step2: Substitute given values

$\theta = 75^\circ$, $r = 24$. Substitute into the formula:
$\text{Sector Area} = \frac{75^\circ}{360^\circ} \times \pi \times (24)^2$

Step3: Simplify the expression

First calculate $(24)^2 = 576$, then $\frac{75}{360} = \frac{5}{24}$.
$\text{Sector Area} = \frac{5}{24} \times \pi \times 576 = 5 \times 24 \pi = 120\pi$

Answer:

B. $120\pi$