1) For a cube the girth plus the longest side is 5s, where s is the length of the side.
So for the largest cube:
2) Let the side of the square base be s and the length be l, then:
The volume is:
V=s^2 x l=s^2 (108-4s)
The largest volume corresponds to one of the solutions of dV/ds=0, so:
216 s -12s^2=0,
one root is s=0, which is not the one we want, the other is s=216/12=18 inches,
from which we get l=36 inches.
3) solution method is similar to 2)