For solving this problem we need to remember the generic formula. If we have a circle sector with angle x (in degrees),
[tex]\text{Area of S}=(radius)^2\cdot\pi\cdot(\frac{angle}{360})[/tex]
The trick of this exercise is that our angle is expressed in degrees (°). Be careful!
Let's compute the solution:
[tex]Area\text{ of our sector }=(16\cdot\pi)^2\cdot\pi\cdot(\frac{240}{360})=16^2\cdot\pi^2\cdot\pi\cdot(\frac{2}{3})=\pi^3\cdot(\frac{512}{3})=\frac{512}{3}\cdot\pi^3[/tex]
That's the final answer.
Comment: For every exercise of this kind you only need to apply the formula I provided you above. If the angle is in radians, the formula is
[tex]\text{ Area of sector }=\frac{1}{2}(radius)^2\cdot(angle)[/tex]
