Posted by **Anonymous** on Sunday, March 27, 2011 at 5:39pm.

An open box of maximum volume is to be made from a square piece of cardboard, 24 inches on each side, by cutting equal squares from the corners and turning up the sides to make the box.

(a) Express the volume V of the box as a function of x, where x is edge length of the square cut-outs.

(b) What are the dimensions of the box that enclose the largest possible volume? State your answer in the form length by width by height.

(c) What is the maximum volume?

- calculus -
**Reiny**, Sunday, March 27, 2011 at 8:12pm
let each side of the equal squares be x inches

length of box = 24-2x

width of box = 24-2x

height of box = x

a) Volume = x(24-2x)(24-2x)

b) expand the volume equation, then take the first derivative.

Set that derivative equal to zero. You will have a quadratic equation. Take the positive answer which lies between 0 and 12

c) put the answer from b) into the volume equation and evaluate.

- calculus -
**jovelyn entera**, Wednesday, January 11, 2012 at 8:26pm
20>o

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