Posted by **danny** on Thursday, September 27, 2012 at 11:36pm.

An open box is made from a square piece of cardboard 20 inches on a side by cutting identical squares from the corners and turning up the sides.(a) Express the volume of the box, V , as a function of the length of the side of the square cut from each corner, x. (b) Find and interpret V (1),V (2),V (3),V (4), and V (5). What is happening to the volume of the box as the length of the side of the square cut increases? (c) Find the domain of V.

- college algebra -
**Steve**, Friday, September 28, 2012 at 11:18am
v = x(20-2x)^2

using what you know about the shape of cubic curves, clearly there is a maximum volume for 0 <= x <= 10 (this is also the domain of v)

Naturally, volume is zero when x=0 and when x=10.

A little checking of values will show that v(x) is max when x = 10/3.

## Answer this Question

## Related Questions

- Calculus - A box with an open top is to be made from a square piece of cardboard...
- calculus - An open box of maximum volume is to be made from a square piece of ...
- Math - A cardboard manufacturer wishes to make open boxes from square pieces of ...
- college algebra word problem - An open box is made from a square piece of ...
- Engineering - A box with an open top is to be made from a square piece of ...
- calculus - An Open Box Of Maximum Volume Is To Be Made From A Square Piece Of ...
- Math - An open box is to be made from a 11 inch by 11 inch piece of cardboad. ...
- Calculus - an open box is made by cutting out squares from the corners of a ...
- Precalculus - From a rectangular piece of cardboard having dimensions a × b, ...
- calculus - An open box is to be made from a square piece of cardboard, 32 inches...