The given information is:
Circle O has a radius r=24 units.
Arc XY located on the circle has a central angle of 75°.
A diagram of the situation is:
We need to find the area of the yellow-shaded region.
We can apply the following formula:
[tex]A=\frac{arcXY}{360\degree}\cdot\pi r^2[/tex]
Replace the known values and solve:
[tex]\begin{gathered} A=\frac{75\degree}{360\degree}\cdot\pi\cdot24^2 \\ A=\frac{5}{24}\cdot\pi\cdot24^{}\cdot24 \\ \text{Simplify 24}/24=1 \\ A=5\cdot\pi\cdot24 \\ A=120\pi \end{gathered}[/tex]
The answer is B. 120pi
