SOLUTION: What is the length of the edge of a cube if, after a slice 1 inch thick is cut from one side, the volume remaining is 294 cubic inches?

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Question 229540: What is the length of the edge of a cube if, after a slice 1 inch thick is cut from one side, the volume remaining is 294 cubic inches?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
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%5E2+%2A+%28l-1%29+=+294
l%5E3+-+l%5E2+=+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%5E3+-+l%5E2+=+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