Posted by **Jemima** on Thursday, July 19, 2012 at 11:44pm.

by cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, the cardboard may be turned into an open box. if the cardboard is 16 inches long and 10 inches wide, find the dimensions of the box that will yield the max volume. what is the max volume?

- calc -
**Reiny**, Friday, July 20, 2012 at 9:26am
let each side of the square to be cut out be x inches

length of base = 16-2x

width of base = 10-2x

height of box = x inches

V = x(16-2x)(10-2x) , where 0 < x < 5

I would now expand that to get a cubic

take the derivative, which is a quadratic,

set the derivative equal to zero and solve for x

Very straight forward question, most Calculus texts use that question as an introduction to optimization.

## Answer this Question

## Related Questions

- calculus - By cutting away identical squares from each corner of a rectangular ...
- calculus optimization problem - by cutting away identical squares from each ...
- Calculus - By cutting away identical squares from each corner of a rectangular ...
- math - By cutting away identical squares from each corner of a rectangular ...
- Math - A box with an open top is to be made by cutting 5-inch squares from the ...
- math - a piece of cardboard is twice as it is wide. It is to be made into a box ...
- PRE-CALCULUS - AN OPEN BOX IS FORMED BY CUTTING SQUARES OUT OF A PIECE OF ...
- math - an open box is to be formed out of a rectangular piece of cardboard whose...
- Calc - You want to make a rectangular box, open at the top, by cutting the same ...
- algebra - A rectangular piece of cardboard is 2 units longer than it is wide? ...