Min/Max Surface Area Cubes (chk anwser)

A mass of clay of volume $\displaystyle 432 in.^3 $is formed into two cubes. What is the minimum possible total surface area of the two cubes? What is the maximum?

(A) The minimum total surface area is obtained by making one cube as small as possible, $\displaystyle .01^3$, and the second cube $\displaystyle 7.5595^3$. The combined total surface area of these two cubes is (0.06+342.8) = 342.86.

The maximum total surface area can be reached with two equal cubes. $\displaystyle 6^3$, for each cube. The combined total surface area of these two cubes is $\displaystyle (216^2)$ = 432.