SOLUTION: I'm very bad at word problems and don't even know where to start so any help would be greatly appreciated. The question is... A closed box with a square base is required to have

Algebra ->  Volume -> SOLUTION: I'm very bad at word problems and don't even know where to start so any help would be greatly appreciated. The question is... A closed box with a square base is required to have      Log On


   

Question 299128: I'm very bad at word problems and don't even know where to start so any help would be greatly appreciated. The question is...
A closed box with a square base is required to have a volume of 50 cubic feet. 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.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Since you say nothing about the height of the box, we'll let h = the height.
The volume, V of such a box can be expressed by:
V+=+hx%5E2 and this is given as 50 cubic feet so...
50+=+hx%5E2 or x%5E2+=+50%2Fh
The surface area of the box A will define how much material is required to fabricate the box.
The box will have four equal faces (sides) and a top & bottom (both equal) for a total of six faces.
We need to determine the area of each of these face and then find their sum to obtain the total surface area and, thus, the amount of material (A) required to fabricate the box.
The top and bottom surfaces will each measure x times x for a total surface area of 2x%5E2sq.ft..
The four equal faces will each measure x times h for a total surface area of 4hx, so the sum of these is:
A+=+2x%5E2%2B4hxsq.ft.
Now if the box is really a cube and h+=+x, then...
A+=+6x%5E2sq.ft.