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