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A computer manufacturing company makes rectangular-shaped boxes for their system units.
The boxes have square bottoms with a height of h inches.
The volume of these boxes is given by the function V=h³-6h²+9h.
Note: Volume = length x width x height; Area = length x width a.
Find the expression for finding the length of each side of the square bottom b.
Find the area of the square bottom and the volume of the box if the company needs
to enclose a system unit with a height of 18 inches.
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The formula for the box volume is
V = x*x*h = = = .
It implies, after canceling the common factor h, that the area of the base of the square box is
area = .
Hence, the side of the square base is x = | h-3 |.
It is the sought expression for the square side of the box.
Notice the absolute value sign in the last formula.
If the height is 18 inches (h = 18 in), then
the base of the box has the are of = 15^2 = 225 square inches
and the volume of the box is 15*15*18 = 4050 cubic inches.
Solved.