Math
posted by tammy on .
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.

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 
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