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.

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- Jul 20th 2011, 12:20 AMgrooverandshakerCuboid question.
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. - Jul 20th 2011, 12:47 AMProve ItRe: Cuboid question.
- Jul 20th 2011, 01:12 AMgrooverandshakerRe: Cuboid question.
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. - Jul 20th 2011, 01:17 AMProve ItRe: Cuboid question.
- Jul 20th 2011, 01:23 AMgrooverandshakerRe: Cuboid question.
Um, I'm not too sure.

Would it be 2x^2+4xh ... - Jul 20th 2011, 01:25 AMProve ItRe: Cuboid question.
- Jul 20th 2011, 01:32 AMgrooverandshakerRe: Cuboid question.
Ok so that'll end up being h=(75 - x^2)/2x.

Do I need to now sub this into something before I can start with the second question? - Jul 20th 2011, 01:36 AMProve ItRe: Cuboid question.
Right, now how would you evaluate the volume of the cuboid?

- Jul 20th 2011, 01:44 AMgrooverandshakerRe: Cuboid question.
I don't really know...

The volume of the cuboid would maybe be h*l*w.

So I spose that would be x^2*h.

But, I don't think that's right. - Jul 20th 2011, 01:45 AMProve ItRe: Cuboid question.