If the area of a circle is 616cm square, calculate the area of the sector with sector angle 60 degrees.

A 60 degree sector  comprises 1/6 of the circle's area , so

(1/6) * 616 =  about  102.66 cm^2

I'm not a native english speaker, so I hope that I got this question right.

You could go two different ways

First: \(\frac{360}{60} = 6\)

this means your sector is 1/6 of the whole circle.

So \(\frac{616cm^2}{6} = 102.67cm^2 \)

Second way: 

\(A = \pi r^2 \\ r = \sqrt{\frac{A}{\pi}}\\ r = 14cm \)

Angle of sector = (A*360) / Pi  * r^2

\(Angle \ of \ sector = \frac{(A \cdot 360)}{\pi r^2}\)

which makes

 \( A = \frac{Angle \ of \ sector \cdot \pi \cdot r^2 }{360} \\ A = 102.63cm^2\)

The difference between both is because rounding, you can use arbitrary precision when doing it yourself.