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Find the formula for the volume of the box

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Squares are cut from a rectangular sheet of cardboard that is 48 by 33 inches. The sides are folded up to form an open-topped box
a) find the formula for the volume of the box in terms of x, the lengths of the sides of the squares.
b) Give the meaningful domain of x.
c) The volume of the box is 4000 cubic inches. Find all values of x that will produce a box with this volume.
d) Give the dimensions of the boxes with a volume of 4000 cubic inches. That is, using your answers from above (there are two boxes possible!) give L x W x H for each box.

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Each step is shown. A calculator is necessary for some of the calculations.

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a)
Since each side has 2 squares, we get the following dimensions for the box:
L = 48 - 2x
W = 33 - 2x
H = x
The formula is:
V = x ( 48 - 2x) (33 - 2x)

b)
The height, length and width of the box must all be positive, otherwise the box would ...

Solution provided by:
J Pye, MSc
Education
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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