Question 229540
Not sure of an easy way to do this one other than trial and error or plotting
Let l be the original length of one side
After cutting off one inch, the new volume is 294
So
{{{l^2 * (l-1) = 294}}}
{{{l^3 - l^2 = 294}}}
Let's try 5
Does 125 - 25 = 294? Nope, too small
Try 10
Does 1000 - 100 = 294? Nope too big
Try 7
Does 
343 - 49 = 294? Yepper. So the answer is 7.

You could also plot {{{l^3 - l^2 = 294}}}
See this URL
http://www.wolframalpha.com/input/?i=l^3+-+l^2+%3D+294

There may be a more elegant path using algebra proper, but sometimes the easiest path to a solution isn't the most elegant