Consider the extrusion of a cylindrical billet, and compute the following.
a. Assume the starting billet to have a length of 0.3 m and a diameter of 15 cm. This is extruded into a cylindrical product that is 3 cm in diameter and 7.5 m long (a reduction ratio of 25). Neglecting the areas on the two ends, compute the ratio between the product surface area (wraparound cylinder) and the surface area of the starting billet.
b. How would this ratio change if the product were a square with the same cross-sectional area as that of the 3 cm diameter circle?
c. Consider a cylinder-to-cylinder extrusion with a reduction ratio of R. Derive a general expression of the relative surface areas of product to billet as a function of R.