Answer
$4\ in \times 12\ in \times 15\ in$.
Work Step by Step
Step 1. Use the figure and dimensions given in the exercise, we have the volume as
$V=3x^2(x+11)=720$
Step 2. Use synthetic division or graphing to solve the above equation: $x^3+11x^2-240=0$ or $(x-4)(x^2+15x+60)=0$, thus $x=4\ in$
Step 3. The dimensions of the cube are: $4\ in \times 12\ in \times 15\ in$.