SOLUTION: An open box is to be constructed from a piece of sheet metal by removing a square of side 1 foot from each corner and turning up the edges. If the box is to hold 4 cubic feet, what

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Question 1208729: An open box is to be constructed from a piece of sheet metal by removing a square of side 1 foot from each corner and turning up the edges. If the box is to hold 4 cubic feet, what should the dimensions of the sheet metal be?
Let me see.
I see the word volume. The problem talks about a box.
I need the volume of a rectangular box formula.
V = length x width x height
or V = lwh for short.
Length = x - 24
Width = x - 24
Height is 12.
My setup is as follows:
Let x = dimensions of the sheet metal
V = (x - 24)(x - 24)(12)
Is my volume setup correct?
Found 3 solutions by timofer, greenestamps, ikleyn:
Answer by timofer(105)   (Show Source): You can put this solution on YOUR website!
Maybe; but since description only uses foot, or feet, square sheet would be 4 feet by 4 feet.

Your setup looks ok on first inspection but your work appears to use inches instead of feet.
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


I don't know why you would change the given description in feet to inches -- it won't change the solution, but it will mean working with larger numbers, which makes the work harder.

But your setup is fine -- as far as you have taken it. The last thing you show in your work is

V = (x - 24)(x - 24)(12)

I hope you are not planning on using the problem description to set V = 4 in your equation to solve the problem....
Answer by ikleyn(52812)   (Show Source): You can put this solution on YOUR website!
.

In this post, some things just shock me.

First, the formulation of the problem is mathematically incomplete (which in Math language means INCORRECT).

To be complete and correct, the problem must say that the original piece of metal is a square.

Then we know that only one dimension should be determined.


Second thing is how you treat the problem.

Without any necessity, without any motivation and without any explanations, you replace feet by inches. 

The normal treatment is to declare that you look for the length x of the side 
of the metal sheet in feet and then to write an equation for the volume

    (x-2)*(x-2)*1 = 4  cubic feet,

which gives

     = 4,

    x - 2 =  = 2,

    x = 2 + 2 = 4.   


ANSWER.  The original peace of metal is a square with the side length of 4 ft.

Solved, without making/creating any artificial difficulties.



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