One Geometrical Problem

A chemical engineer who is designing a drug factory has to solve a problem which concerns the building of a spherical reservoir over a conical support as shown in Fig. 3.72. For this construction, the total volume must not exceed 5 m. At the same time, the relation between the sphere diameter and the cone height is imposed in accordance with the golden section principle (D = I/5). 

Considering that the fixed volume is V = 5 m, the solution to this system results in the following values for the heights and diameter G = —1.45 m, I = 8.8 m and D = 1.43 m. We can notice here that the value of G is not realistic. 

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