Posted by **kaa** on Friday, January 17, 2014 at 11:16am.

You want to make a rectangular box, open at the top, by cutting the same size square corners out of a rectangular sheet of cardboard and then folding up the sides. The cardboard measures 10 in. by 12 in. What are the dimensions of the box that will have greatest volume if the possible corner cuts measure 1 in., 2 in., 3 in., or 4 in.?

- Calc -
**Steve**, Friday, January 17, 2014 at 11:25am
well, the volume is width * length * height (x)

v = (10-2x)(12-2x)(x)

now plug in x=1,2,3,4 and see which gives the greatest volume

- Calc -
**kaa**, Friday, January 17, 2014 at 11:33am
a.9 in. by 12 in. by 1 in.

b.3 in. by 6 in. by 4 in.

c.7 in. by 10 in. by 2 in.

d.5 in. by 8 in. by 3 in.

c?

- Calc -
**Steve**, Friday, January 17, 2014 at 11:52am
Nope. Think about it. Since the two original dimensions are 8x10, after the cuts, the base of the box will be

8x10

6x8

4x6

2x4

You cannot even get (c) by cutting equal squares from all corners.

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