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a square piece of metal with sides 3m has a square of side 'x' cut out of each corner....

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xdsmith | eNoter

Posted July 10, 2013 at 12:16 AM via web

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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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Mary Joy Ripalda | High School Teacher | (Level 3) Educator

Posted July 10, 2013 at 4:26 AM (Answer #1)

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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.

height=x

length=3-x-x=3-2x

width=3-x-x=3-2x

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

`V=l*w*h`

`V=(3-2x)*(3-2x)*x`

`V=x(3-2x)^2`

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

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