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

• Apr 18th 2009, 11:28 AM
milan
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)!
• Apr 18th 2009, 11:31 AM
stapel
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.
• Apr 18th 2009, 02:29 PM
Kuruma
Hi, Im new here but I think I can help(Hi)

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.
• Apr 18th 2009, 02:50 PM
Kuruma
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...