SOLUTION: An open box is to be constructed from a square piece of sheet metal by removing a square of side 6 inches from each corner and turning up the edges. If the box is to hold 294 cubic

Question 263610: An open box is to be constructed from a square piece of sheet metal by removing a square of side 6 inches from each corner and turning up the edges. If the box is to hold 294 cubic inches, what should be the dimensions of the sheet metal?
Found 2 solutions by drk, stanbon:
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
The original box is x by x
we cut 6 inches off each corner. The new dimensions are (x-12) by (x-12) and the height is 6.
The volume can be expressed as

in our case as

or

dividing by 6 we get

taking a square root we get

add 12 to get
x = 19 inches
dimensions are 19 x 19
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
An open box is to be constructed from a square piece of sheet metal by removing a square of side 6 inches from each corner and turning up the edges.
If the box is to hold 294 cubic inches, what should be the dimensions of the sheet metal?
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Let the sheet metal be x" by x".
Sketch a square that is x by x.
sketch 6 by 6 squares in each of its corners.
Imagine cutting out those four squares.
Imagine folding up the four sides to form a box.
---------
The base of the box is (x-2*6)^2 sq in.
The height of the box is 6 in
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Volume = 6(x-12)^2 = 294
(x-12)^2 = 49
x-12 = 7
x = 19"
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Cheers,
Stan H.
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