A cuboid has a total surface area of 150cm^2 with a square base x cm.
Show that the height, h cm, of the cuboid is given by h=(75-x^2)/(2x).
Express the volume of the cuboid in terms of x.
Hence determine its maximum volume as x varies.
To be completely honest, I have no idea where to start.
But for the second bit, I think I would do 150cm^2 * (75-x^2)/(2x) to find the volume, maybe??
And then for the third bit, I'll find the derivative, let it equal 0 to find x and once I find x sub it back into the volume equation.
I just don't really understand how to do the first bit.