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 − 3 2 s2 cot(θ) + 3s2 3 / 2 csc(θ) where s, the length of the sides of the hexagon, and h, the height, are constants. (a) calculate ds/dθ. ds dθ = correct: your answer is correct. (b) what angle should the bees prefer? † (round your answer to two decimal places.) ° (c) determine the minimum surface area of the cell (in terms of s and h).