In a beehive, each cell is a regular hexagonal prism, open at one end with a trihedral angle at the other end as in the figure. 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 θ is amazingly consistent. Based on the geometry of the cell, it can be shown that the surface area s is given by s = 6sh-y cot@) + (3s2v/5 / 2) csc(㮠where s, the length of the sides of the hexagon, and h, the height, are constants. trihedral angle θ rear of cell front of cell (a) Calculate ds/d9. ds (b) What angle should the bees prefer?t (Round your answer to two decimal places.) (c) Determine the minimum surface area of the cell (in terms of s and h)