A single crystal boule of silicon is grown by the Czochralski process to an average diameter of 320 mm with length = 1500 mm. The seed and tang ends are removed, which reduces the length to 1150 mm. The diameter is ground to 300 mm. A 90- mm-wide flat is ground on the surface that extends from one end to the other. The ingot is then sliced into wafers of thickness = 0.50 mm, using an abrasive saw blade whose thickness = 0.33 mm. Assuming that the seed and tang portions cut off the ends of the starting boule were conical in shape, determine

(a) the original volume of the boule, mm3;

(b) how many wafers are cut from it, assuming the entire 1150 mm length can be sliced; and

(c) the volumetric proportion of silicon in the starting boule that is wasted during processing.