Answer:
[tex]327.08cm^{2}[/tex]
Step-by-step explanation:
The area of a circular sector is calculated with this expression:
[tex]A=\frac{\pi R^{2}\alpha^{\°}}{360\°}}[/tex]; where [tex]\alpha^{\°}[/tex] the central angle, and [tex]R[/tex] is the radius.
Then, we replace all values and solve for A:
[tex]A=\frac{\pi R^{2}\alpha^{\°}}{360\°}}= \frac{(12.5)^{2}(\frac{4\pi}{3}\pi ) }{360\°}\\A= \frac{2054.1}{6.28} =327.08cm^{2}[/tex]
In the problem, we used [tex]\pi=3.14[/tex], and [tex]360\°=6.28[/tex], because the problem is asking to use radians, and we cannot operate radians with grades, it would be wrong.
Therefore, the answer is [tex]327.08cm^{2}[/tex]
