SOLUTION: 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

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Question 1186360: 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​.

Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
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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 = h%5E3+-+6h%5E2+%2B+9h = %28h%5E2-6h%2B9%29%2Ah = %28h-3%29%5E2%2Ah.


It implies, after canceling the common factor h, that the area of the base of the square box is


    area = %28h-3%29%5E2.


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  %2818-3%29%5E2 = 15^2 = 225 square inches

        and the volume of the box is  15*15*18 = 4050 cubic inches.

Solved.