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 open-topped 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 = (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

- 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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