Get Real Math Robinson Metal Geometric measurements

The NEW Manufacturing Alliance's "Get Real Math!" filmed at Robinson Metal in De Pere, Wisconsin. The manufacturing-related math problems showcase the following Common Core Skills:
4.MD Geometric measurement: understand concepts of angle and measure angles.
7G Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

HSG.C
B5. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.