Math CentralQuandaries & Queries


Rita, a student:

An open box with a square base is needed to have a volume of 10 cubic feet.

(a) Express the amount A of material used to make such a box
as a function of the length x of a side of the square base.

(b) How much material is needed for a base 1 foot by 1 foot?

Hi Rita,

Here is an approximate diagram for your problem:

Let's let x be the sides of the square base and h be the height of the box. So for our formulae for our open box will be


10 ft=(x)(x)(h)

10 ft=x2h
The area of the base is (x)(x) and each of the four sides is (x)(h)

A = 4xh + x2

Since the questions asks us to write the area in terms of one variable, x, you can manipulate the volume formula solving for h and substitute it into the area formula.

Hope this helps,


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