Posted by **Isaac** on Tuesday, August 9, 2011 at 9:08am.

A manufacturer constructs open boxes from sheets of cardboard that are 6 inches square by cutting small squares from the corners and folding up the sides. The Research and Development Department asks you to determine the size of the square that produces a box of greatest volume. Proceed as follows. Let x be the length of a side of the square to be cut and V be the volume of the resulting box. Show that V = x(6-2x)^2. I don't understand how I'm suppose to show what they are asking.

- Calculus -
**Reiny**, Tuesday, August 9, 2011 at 9:44am
make a sketch of a 6 by 6 square.

Draw squares at each corner of x by x

(You could actually cut them out with scissors)

This would allow you to fold up the sides to form a box

Wouldn't each side of the base remaining be 6 - 2x, since x units were taken away at each end ?

Wouldn't the height of the box be x ?

volume = base x height

= (6-2x)(6-2x(x)

= x(6-2x)^2

- Calculus -
**Isaac**, Tuesday, August 9, 2011 at 10:09am
I just wasn't sure if the answer was simply a sketch, 6 - 2x each side with the cut-outs. Thanks!!

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