Posted by **Jamie** on Tuesday, June 23, 2009 at 8:31pm.

Suppose you take a piece of cardboard measuring 7 inches by 7 inches, cut out square corners with sides x inches long, and then fold up the cardboard to make an open box. Express the volume V of the box as a function of x.

- Math -
**Reiny**, Tuesday, June 23, 2009 at 8:36pm
did you make a sketch?

isn't the base after the cut-out (7-2x) by (7-2x) and isn't the height of the box x inches?

volume of box = base area x height

=

- Math -
**Jamie**, Tuesday, June 23, 2009 at 8:59pm
Yes so my conclusion is that

V(x) = x (7 – 2x)^2

is this correct?

- Math -
**Reiny**, Tuesday, June 23, 2009 at 9:06pm
correct

- Math -
**Jamie**, Tuesday, June 23, 2009 at 9:09pm
Thanks! I knew I would get this stuff! Thanks for your help!

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