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!

## Answer this Question

## Related Questions

- Math - Suppose you take a piece of cardboard measuring 7 inches by 7 inches, cut...
- Math - A cardboard manufacturer wishes to make open boxes from square pieces of ...
- Math - Arlan needs to create a box from a piece of cardboard. The dimensions of...
- Algebra - A rectangular piece of cardboard is 15 inches longer than it is wide. ...
- calculus - an open rectangular box is to be made from a piece of cardboard 8 ...
- Calculas - an open box is to be made from a square piece of cardboard whose ...
- algebra 2 - you can make an open box from a piece of flat cardboard. First cut ...
- Geometry - A square piece of cardboard, 24 inches by 24 inches, is to be made ...
- Calculus (Optimization) - A rectangular piece of cardboard, 8 inches by 14 ...
- algebra - Volume of a Box A box is constructed by cutting out square corners of ...