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. 5π
c. 120π
d. 51π

Explanation:

Step1: Recall the formula for the area of a sector

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

Step2: Substitute the given values into the formula

Given that \(r = 24\) units and \(\theta=75^{\circ}\).

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Answer:

C. \(120\pi\)