front 3 of cell In a beehive, each ell is a regular hexagonal prism, open at one end with a trihedal angle at the other end. It is believed that bees form their cells in such a way as to minimize the surface area for a given volume, thus using the least amount of wax in cell construction. Examination of these cells has shown that the measure of the apex angle 9 is amazingly consistent. Based on the geometry of the cell, it can be shown that the surface area S is given by S = 6s gazcot + (Sszx/g/Z) cscB where s, the length of the sides of the hexagon, and h, the height, are constants. (a) Calculate dS/dB. (Your answer may depend on s, h, and I (use t instead of theta. (b) What angle should bees prefer (in radians)? (c) Determine the minimum surface area of the cell (Your answer may depend 011 s and h)