Posted by **Anonymous** on Friday, April 20, 2012 at 1:31pm.

Take an 8.5 by 14-inch piece of paper and cut out four equal squares from the corners. Fold up the sides to create an open box. Find the dimensions of the box that has maximum volume. (Enter your answers as a comma-separated list. Round your answer to three decimal places.)

- calculus -
**Steve**, Friday, April 20, 2012 at 2:14pm
cut squares of length x

v = x(8.5-2x)^2 = 72.25x - 34x^2 + 4x^3

dv/dx = 72.25 -68x + 12x^2

max/min achieved at x = 17/12 or 17/4

Just knowing about the shape of cubics, it's clear that 17/12 is where the max volume occurs.

So, the box is 8.5-17/6 x 8.5-17/6 x 17/12 = 17/3 x 17/3 x 17/12

## Answer This Question

## Related Questions

- math - Take an 17 by 11-inch piece of paper and cut out four equal squares from ...
- functions - Given a 10 cm by 20 cm piece of paper, if you cut out four equal ...
- Algebra - Given a 10 cm by 20 cm piece of paper, if you cut out four equal ...
- calculus - An open box is to be made out of a 8-inch by 14-inch piece of ...
- Calc - An open box is to be made out of a 10-inch by 16-inch piece of cardboard ...
- calculus - An open box is to be made out of a 10-inch by 14-inch piece of ...
- algebra 2 - you can make an open box from a piece of flat cardboard. First cut ...
- Math - An open-topped box can be created by cutting congruent squares from each ...
- Calculus - An open top box is made by cutting congruent squares from the corners...
- calculus - You have an 8.5 inch by 11 inch piece of paper. You need to cut out ...

More Related Questions