# Thread: volume of cilinder maximum problem. exam tmw!!!

1. ## volume of cilinder maximum problem. exam tmw!!!

a cilindrical container of height h cm and radius r cm has both ends closed. It is produced using exactly 54pi cm2 of plastic.

i) express h in terms of r
ii) find the maximum possible volume of the container in terms of Pi.

I did the first part, i need the steps for part ii)!

2. You have the formula for the volume V in terms of h and of r. You've solved for h in terms of r.

Take the expression for h "in terms of r", and plug this in for "h" in the volume formula. This gives you the volume in terms only of r.

Differentiate, etc.

3. Hi, Im new here but I think I can help

The volume of the cylinder is given by the expression:

$\displaystyle V=\pi*r^2*h$

But, as you have h in terms of r, you can get:

$\displaystyle V=\pi\,r^2\,({54 \over 2r}-r)$

Now, if you derivate the above expression and equal it to 0 you can get the answer I think, Ill do it and post it here.

4. After a few calculations, I got a radius of 3, which leads us to a volume

$\displaystyle V=54\pi\,cm^3$

I`m not sure, but, if anyone wants to check it out...