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Maximize Volume of a Box

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Maximizing the Volume of a Box, a selection of answers from the Dr. Math archives.

Maximum Volume of a Box
A rectangular sheet of cardboard measures 16cm by 6cm. Equal squares are cut out of each corner and the sides are turned up to form an open rectangular box. What is the maximum volume of the box?

Maximizing the Volume of a Box
What dimensions should a rectangular piece of paper have to maximize the volume of the box made by cutting the corners out and folding?

Maximizing the Volume of a Box: Find Size of Square Cutout
If I have a rectangular card of size AxB, how can I find the size of the square cutout that maximizes the volume of the box produced when the edges are folded up?

Open Box Problem
Find the formula for the greatest volume box you can make from a sheet of cardboard with different-sized corners cut out of it.

Maximizing the Volume of a Box
I have a piece of glass that is 14" by 72". What dimensions would I need to make a glass cage with maximum volume?

Maximizing Volume of a Cereal Box
Why are cereal boxes the size they are? Is it just to maximize volume?

Maximum Volume: Making a Box from a Sheet of Paper
I am making a box out of a sheet of paper by cutting squares out of the corners. How can I show that the largest possible volume occurs when the side of the square is 1/6 the length of the sheet of paper?

Dimensions of a Cardboard Box
A box with a square bottom and a volume of 2000 centimeters can be made by cutting 5-centimeter squares from the corners of a piece of cardboard...

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