Posted by **Oswaldo** on Tuesday, October 19, 2010 at 11:01am.

A SHEET OF CARDBOARD 180 INCHES SQUARE IS USED to make an open box by cutting squares of equal size from the corners and folding up the sides, what size squares should be cut to obtain a box with the largest possible volume?

- Calculus -
**MathMate**, Tuesday, October 19, 2010 at 11:37am
If x represents the side of each of the 4 little squares cut from the corners, then the dimensions of the box would be (180-2x), (180-2x) and x.

Volume,

V(x)=x(180-2x)²

Find V'(x)=dV(x)/dx and equate to zero. Solve for x. Retain only positive root, x0.

To make sure the value of x is maximum, Find V"(x)=d²V(x)/dx² and evaluate V"(x0).

If V"(x0)<0, V(x0) is at its maximum.

Post your answer for a check if you wish.

- Calculus -
**Anonymous**, Wednesday, March 30, 2011 at 10:11pm
180

## Answer This Question

## Related Questions

- Calculus - A square sheet of cardboard with a side 16 inches is used to make an ...
- math - a rectangular sheet of cardboard 4m by 2m is used to make an open box by ...
- Math Wrod Problem - 1. A long strip of copper 8 inches wide is to be made into a...
- algebra - Open-top box. Thomas is going to make an open-top box by cutting equal...
- Math - An open box is to be made from a 10-ft by 14-ft rectangular piece of ...
- math - open top rectangular box made from 35 x 35 inch piece of sheet metal by ...
- Calculus - A box with an open top is to be made from a square piece of cardboard...
- Calculas - an open box is to be made from a square piece of cardboard whose ...
- Math--Please Help - A pizza box with a square base is to be made from a ...
- algebra 2 - you can make an open box from a piece of flat cardboard. First cut ...

More Related Questions