Answer
$7\ in$
Work Step by Step
Step 1. Let $x$ be the length of the edge of the cube. The dimensions after the cut will be $x-1$ by $x$ by $x$
Step 2. The volume of the remaining is $x^2(x-1)=294$ or $x^3-x^2-294=0$
Step 3. We can solve the equation graphically as shown in the figure to get $x=7\ in$
