Question

If 1100 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

Answer 1

got a picture?

Answer 2

if you call the lenght of the base \(x\) and the height \(h\) then the base has area \(x^2\) and the four sides have area \(xh\) making the total
\[x^2+4xh\]

Answer 3

since you know that total is \(1100\) you can set \[x^2+4xh=1100\] and solve for \(h\) in terms of \(x\)

Answer 4

pretty much in your head
i get
\[h=\frac{1100-x^2}{x}\]

Answer 5

then the volume is
\[V=x^2h\] but now it is
\[V(x)=x^2(\frac{1100-x^2}{x})\] maximize that one

Answer 6

you good from there?