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. 51π D. 120π

To find the area of the sector associated with arc XY, we can use the formula for the area of a sector, which is given by: \[ \text{Area} = \frac{\theta}{360^\circ} \times \pi r^2 \] where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle. In this case, \(\theta = 75^\circ\) and \(r = 24\) units. Plugging in these values: \[ \text{Area} = \frac{75}{360} \times \pi \times 24^2 \] Calculating \(24^2\): \[ 24^2 = 576 \] Now substituting this back into the formula: \[ \text{Area} = \frac{75}{360} \times \pi \times 576 \] This simplifies to: \[ \text{Area} = \frac{75 \times 576 \pi}{360} \] Now, simplifying \(\frac{75}{360}\): \[ \frac{75}{360} = \frac{5}{24} \] So we have: \[ \text{Area} = \frac{5}{24} \times 576 \pi \] Calculating \(\frac{5 \times 576}{24}\): \[ 576 \div 24 = 24 \quad \text{and thus} \quad 5 \times 24 = 120 \] Finally, we have: \[ \text{Area} = 120\pi \] Therefore, the area of the associated sector is \( \boxed{120\pi} \).