SOLUTION: The two congruent squares are removed from one of a rectangular 10 in by 20 in a piece of cardboard. Two congruent rectangles are removed from the other end. Determine the equation

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Question 1172972: The two congruent squares are removed from one of a rectangular 10 in by 20 in a piece of cardboard. Two congruent rectangles are removed from the other end. Determine the equation of the volume of the resulting box as a function of x. What is the domain of the function?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52748) About Me  (Show Source):
You can put this solution on YOUR website!
.

The volume is  V = x*(20-2x)*(10-2x).


The domain is  0 < x < 5,  making the factors positive.

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Read the necessary addition from the post by @greenestamps.

I fully support it (!)



Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


Faulty statement of the problem!

(1) It is not stated how the box is formed after cutting the pieces out of each end of the piece of cardboard -- although this is a common type of problem, so it is obvious
(2) It is not stated what size pieces are cut out of each end
(3) A box is only formed when the pieces cut out of all four corners are congruent squares. Cutting congruent squares out of one end and congruent rectangles out of the other end will not produce a box.
(4) Since x is nowhere defined, it is of course impossible to write and expression for the volume of the box as a function of x.