What angle should bees prefer (in radians)Determine the minimum surface area of the cell trihedralrearof cellangle 0hb.frontof cellSIn 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 tominimize 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 apexangle 0 is amazingly consistent. Based on the geometry of the cell, it can be shown that the surface area S is given by3S = 6shs? cot 0 + (3s² v3/2) csc 02where s, the length of the sides of the hexagon, and h, the height, are constants.(a) Calculate dS/d0. (Your answer may depend on s, h, andt (use t instead of theta)).

Answered: What angle should bees prefer (in…

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter64: Volumes Of Spheres And Composite Solid Figures

Section: Chapter Questions

Problem 27A

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What angle should bees prefer (in radians) Determine the minimum surface area of the cell