A manufacturer cuts squares from the corners of a rectangular piece of sheet metal that measures 5 centimeters by 3 centimeters. The manufacturer then folds the metal upward to make an open-topped box. Letting x represent the side-lengths (in centimeters) of the squares, find the value of that maximizes the volume enclosed by this box. Then give the maximum volume. Round your responses to two decimal places.A manufacturer cuts squares from the corners of a rectangular piece of sheet metal that measures...?
the dimention of the base of the box:
L = (5 - 2x)
W = (3 - 2x)
the height is x
V = (5 - 2x) (3 - 2x) x
V = 4x^3 - 16x^2 + 15x
find the derivative and set it equal to 0
0 = 12x^2 - 32x + 15
use quadratic formula and you'll get x =~ 0.61cm
V = (5 - 2*.61) (3 - 2*.61) (.61)
V =~ 4.10 cm^3
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