a square piece of metal with sides 3m has a square of side 'x' cut out of each corner. The metal is then folded up to form a rectangular prism. Find volume in terms of x   ans: v=x(3-2x)^2

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lemjay | High School Teacher | (Level 3) Senior Educator

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Refer to the figure below that illustrates the problem.

Since a square with side x is cut out from each corner of the metal, then the resulting box would have the following dimension.




Then, substitute these to the formula of volume of a box which is:




Hence, the volume of the box formed is  ` V=x(3-2x)^2` .

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