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.

Answer 1

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
=

Answer 2

Yes so my conclusion is that

V(x) = x (7 – 2x)^2

is this correct?

Answer 3

correct

Answer 4

Thanks! I knew I would get this stuff! Thanks for your help!