Find the formula for the described function and state its domain. An open rectangular box with a volume of 8 cubic meters has a square base. Express the surface area of the box as a function of S(x) of the length x of a side of the base.

Answer 1

from the volume,
8 = x * x * h
h = 8/(x^2)
therefore,
surface area = 2lw + 2lh + 2wh
where l=length, w=width, h=height
since it's an open box:
S(x) = x^2 + 2[8/(x^2)](x) + 2[8/(x^2)](x)
S(x) = x^2 + 32/x

so there,, :)