Consider a rectangular box B that has a bottom and sides but no top and has minimal surface area among all boxes with fixed volume V = 64 m³.

(a) Do you think B is a cube as in the solution to Exercise 54? If not, how would its shape differ from a cube?

Data From Exercise 54

Show that the rectangular box (including the top and bottom) with fixed volume V = 27 m³ and smallest possible surface area is a cube (Figure 25).

(b) Find the dimensions of B and compare with your response to (a).

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X y Z