
Optimization Help?
If 30,000 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
in cm3
I've tried it and can't seem to get it right. So basically 30,000 is the surface area? If so, i did Surface area = 6x^2
But since the top is missing, it should be SA = 5x^2
http://math2.org/math/geometry/cube.gif
then i did 30000 = 5x^2
x = sqrt(6000) = 77.4597
Volume = lwh
Volume = x^3
Volume = 77.4597^3
Volume = 232.379
But it says that is wrong. Where did I mess up and how do I get the right answer? Thanks.
EDIT: nevermind, i did more work on it and tried a different method. i got the right answer. (500,000)