SOLUTION: A rectangular box open at the top is to be from a rectangular piece of cardboard 3 inches by 8 inches. What size square should be cut from each corner to form the box with maximum
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Question 1122183: A rectangular box open at the top is to be from a rectangular piece of cardboard 3 inches by 8 inches. What size square should be cut from each corner to form the box with maximum volume? Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! V=l*w*h
draw this out, and cut a square with side x out of each of the 4 corners.
the length of the box will be 8-2x and the width 3-2x. The height is x
The volume is (24-22x+4x^2)*(3-2x)=(24-22x+4x^2)x
=4x^3-22x^2+24x
take the derivative and set equal to 0
0=12x^2-44x+24
divide by 4
3x^2-11x+6=0
(3x-2)(x-3)=0
x=(2/3), and 3, but 3 inches is the entire width, so x=1/3 inch
volume is (6 2/3)(1 2/3) (2/3)=200/27 in^3=7.41 in^3
