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A Single Cell of a Bee's Honey Comb Has the Shape

Question 43

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A single cell of a bee's honey comb has the shape shown.The surface area of this cell is given by A=6hs+32s2(cosθsinθ+3sinθ)A=6 h s+\frac{3}{2} s^{2}\left(\frac{-\cos \theta}{\sin \theta}+\frac{\sqrt{3}}{\sin \theta}\right) where h, s, θ\theta are as shown in the picture.Keeping h and s fixed, for what angle, θ\theta , is the surface area minimal? Round to the nearest one tenth of a degree.  A single cell of a bee's honey comb has the shape shown.The surface area of this cell is given by  A=6 h s+\frac{3}{2} s^{2}\left(\frac{-\cos \theta}{\sin \theta}+\frac{\sqrt{3}}{\sin \theta}\right)  where h, s, \theta  are as shown in the picture.Keeping h and s fixed, for what angle,  \theta , is the surface area minimal? Round to the nearest one tenth of a degree.

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