Notes: an open rectangular box with a volume of 12 ft^3 has a square base. Express the surface area A of the box as a function of the length x of a side...

Saturday, February 6, 2010

an open rectangular box with a volume of 12 ft^3 has a square base. Express the surface area A of the box as a function of the length x of a side...

Hello!

I suppose that "open" means "without the upper side" and that $\displaystyle{x}$ is in feet.

Denote the height as $\displaystyle{h}$ (ft). Then the surface area is $\displaystyle{A}={{x}}^{{2}}+{4}{h}{x}$ (bottom square $\displaystyle{x}$ by $\displaystyle{x}$ and 4 sides $\displaystyle{x}$ by $\displaystyle{h}$ ), and the volume is $\displaystyle{{x}}^{{2}}{h}={12},$ so $\displaystyle{h}=\frac{{12}}{{{x}}^{{2}}}.$