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| Math Central | Quandaries & Queries |
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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 (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
| V=lwh
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,
Janice
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