SOLUTION: The areas of the sides of a rectangular box are 12 in. squaredin.2​, 24 in. squaredin.2​, and 32 in .2. What is the volume of the​ box?
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Question 1023100: The areas of the sides of a rectangular box are 12 in. squaredin.2, 24 in. squaredin.2, and 32 in .2. What is the volume of the box? Answer by robertb(5830) (Show Source):
You can put this solution on YOUR website! Let w = width in inches, h = height in inches, and l = length in inches.
Without loss of generality, let
wh = 12,
hl = 24, and
lw = 32.
The first two equations imply that
==> l = 2w ==> (2w)w = 32 after substitution into the 3rd equation.
==> ==> w = 4 inches.
==> l = 8 inches, and h = 3 inches.
Therefore the volume is 3*4*8 = 96 cubic inches.
