Question

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 open-topped box. Find the maximum possible volume of the box.

Answer 1

x is size of side of square cut out
then height of box x
length = (10-2x)
width =(8-2x)
V = x (10-2x)(8-2x)
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
(3x-5)(x-4) = 0
x = 5/3 or x = 4
x = 4 gives zero volume
so I suspect x = 5/3

Answer 2

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

Answer 3

lol