SOLUTION: An open top box with a square base is to be constructed from a sheet metal in such a way that the completed box is made of 2m^2 of the sheet metal. Express the volume of the box as

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Question 253460: An open top box with a square base is to be constructed from a sheet metal in such a way that the completed box is made of 2m^2 of the sheet metal. Express the volume of the box as a function of the width of the base.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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An open top box with a square base is to be constructed from a sheet metal in such a way that the completed box is made of 2m^2 of the sheet metal.
Express the volume of the box as a function of the width of the base.
:
The side of a square piece of sheet metal of 2 sq/m = sqrt%282%29 m
:
Let x = side of the square base of the box
:
let h = side of the 4 small squares removed from the square sheet to make the box
Also h = the height of the open box
:
x = sqrt%282%29+-+2h
solve in terms of h
2h = sqrt%282%29+-+x
:
h = %28sqrt%282%29+-+x%29%2F2
:
Vol = x^2 * h
replace h with %28sqrt%282%29+-+x%29%2F2
:
V(x) = x%5E2+%2A+%28%28sqrt%282%29+-+x%29%2F2%29
:
:
Max vol occurs when x = .9 m, find h
h = %28sqrt%282%29+-+.9%29%2F2
h = .26 m
:
.9^2 * .26 = .21 cu meters