Question

I have a question:
So! A box has square base and total surface area equal to 12 m2.
(a) Express its volume as a function of x, the length of one side of the base.
(b) Find the maximum volume of such a box.
I am not sure how to set up this problem. Do I need to use the volume formula of a box or something to set the equation as a function of x?

Thank you!

Answer 1

volume is the area of the base times the height.
the area of the base is \(x^2\) since it is a square
your job is to find an expression for the length of the height in terms of \(x\)
to do that note the surface area is \(2x^2+4xh=12\)
solve this for \(h\) in terms of \(x\)

Answer 2

you get
\[4xh=12-2x^2\]
\[h=\frac{12-x^2}{4x}=\frac{3}{x}-\frac{x}{4}\]

Answer 3

you get
\[4xh=12-2x^2\]
\[h=\frac{12-x^2}{4x}=\frac{3}{x}-\frac{x}{4}\]

Answer 4

question!!!

Answer 5

multiply by \(x^2\) to get \(V(x)\) then find the max

Answer 6

how did you get the 2x^2 and the 4xh?

Answer 7

Sorry, I am kind of slow at this.

Answer 8

Oh and what happened to the 2 when you were putting the h by itself? shouldn't it be 12-2x^2/4x?

Answer 9

i drew a picture
you have a box
top and bottom have area \(x^2\) and then 4 sides have area \(xh\)