If 600 cm2 of material is available to make a box with a square base and a closed top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000.

Answer 1

If we have base x^2 and height y,

2x^2 + 4xy = 600

v = x^2y = x^2(600-2x^2)/4x
= 150x - x^3/2

Now just find x where v' = 0

Answer 2

0.0

Answer 3

20000