Posted by tammy on Saturday, April 9, 2011 at 6:31pm.
From an 8 inch by 10 inch rectangular sheet of paper, squares of equal size will be cut from each corner. The flaps will then be folded up to form an opentopped box. Find the maximum possible volume of the box.

Math  Damon, Saturday, April 9, 2011 at 7:37pm
x is size of side of square cut out
then height of box x
length = (102x)
width =(82x)
V = x (102x)(82x)
V = x(80  36x + 4x^2)
V = 80 x  36 x^2 + 4 x^3
dV/dx = 80 72 x + 12 x^2
dV/dx = 0 for max or min
so
3x^2  18x + 20 = 0
(3x5)(x4) = 0
x = 5/3 or x = 4
x = 4 gives zero volume
so I suspect x = 5/3

Math  Smile, Thursday, December 11, 2014 at 10:38pm
Damon's answer is almost right, but you have to use the quadratic equation x is 5.055... and 1.472... so basically 1.472. The volume is then about 13.583in^3
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