Question

What is the area of a sector with radius 6" and measure of arc equal to 120°?

Answer 1

Its square area is: 1/3*pi*62 = 12*pi or 37.699 to 3 decimal places

Answer 2

This is one possible approach:
1) calculate the area of the whole circle, of radius 6" .
2) If the central angle (which defines the sector) is measured in degrees (as it is here),
then the area of the sector is

central angle
------------- * area of the circle
360 deg