Constructing An Open Box

mathxyz · 2024-04-27 08:49:57

An open box with a square base is to be made from a square piece of cardboard 24 inches on a side by cutting out a square from each corner and turning up the sides.

Given:

Square = 24 inches on a side.

The little square that have been cut measures x inches by x inches and there are 4 little squares (one on each corner).

Express the volume V of the box as a function of the length x of the side of the square cut from each corner.

Let me see.

Volume of box = (edge)^3.

Area of each little square = x^2.

Length of each side of the square = 24 inches.

We want V(x).

My model is V(x) = (24 - x^2)^3.

You say?

Bob · 2024-04-27 20:16:22

You haven't got the diagram right. Start with a 24 by 24 square. Cut off the corner squares (x by x) so you have a sort of cross. When you fold up the four sides, the base of the box has dimensions (12-2x) by (12-2x) and height x.

Bob

mathxyz · 2024-04-28 01:31:36

Bob wrote:

You haven't got the diagram right. Start with a 24 by 24 square. Cut off the corner squares (x by x) so you have a sort of cross. When you fold up the four sides, the base of the box has dimensions (12-2x) by (12-2x) and height x.
Bob

Ok. By the time I reached this problem, I was exhausted from the previous applications. Honestly, there is nothing more important in mathematics than the skill of forming models or equations or functions from the given data in word problems.

Math Is Fun Forum

#1 2024-04-27 08:49:57

Constructing An Open Box

#2 2024-04-27 20:16:22

Re: Constructing An Open Box

#3 2024-04-28 01:31:36

Re: Constructing An Open Box

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