a six-sided rectangular box has a square base with edges at least 1cm long. Its total surface area for the top, bottom, and four sides is 600cm^2. What is the largest possible volume that such a box can have?

Question

anonymous · Answer

I can't do this thoroughly since it's alot of writing. But it's a basic optimization calculus problem. Find the equation for V, where V is volume. Then derive V to get V'. Then find the critical points of V' where V' = 0. Check the points where V' = 0 and which ever is the highest is the max volume!

anonymous · Answer

U may begin with letting a side of the square base be x so it's surface area is x^2.

The volume will then be this area times the height or length of the box, say h.

If u calculate the total surface area u can get a relationship between x and h.