Answer:
[tex]A(x)=\dfrac{x^3+949104}{x}[/tex]
Step-by-step explanation:
Given a box with a square base and an open top which must have a volume of 237276 cubic centimetre. We want to find a formula for the surface area of the box in terms of only x, the length of one side of the square base.
Let the side length of the base =x
Let the height of the box =h
Since the box has a square base
Volume,
[tex]V=x^2h=237276\\\\h=\dfrac{237276}{x^2}[/tex]
Surface Area of the box = Base Area + Area of 4 sides
[tex]Area, A(x,h)=x^2+4xh[/tex]
Substitute h derived above into A(x,h)
[tex]Area=x^2+4x(\frac{237276}{x^2})\\\\A(x)=x^2+\dfrac{949104}{x}\\\\A(x)=\dfrac{x^3+949104}{x}[/tex]
Therefore, a formula for the surface area of the box in terms of only x, the length of one side of the square base is:
[tex]A(x)=\dfrac{x^3+949104}{x}[/tex]
