A closed cylindrical tank is to be built using 924m^2 of metal. Calculate the radius and height if the volume of the cylinder is to be a maximum.

I just cant get my head around these problems. (Headbang)

Printable View

- Nov 28th 2010, 08:00 AMmanexaA closed cylindrical tank
A closed cylindrical tank is to be built using 924m^2 of metal. Calculate the radius and height if the volume of the cylinder is to be a maximum.

I just cant get my head around these problems. (Headbang) - Nov 28th 2010, 08:10 AMskeeter
- Nov 29th 2010, 05:15 AMmanexa
Hey skeeter

Thanks for the help.

I still don't get it though. I think I will just have to accept that some things in maths are beyond me. (Worried) - Nov 29th 2010, 04:24 PMskeeter
don't give up so easy. this problem is not as bad as you think.

this first equation is the total surface area of a cylinder ...

sub this into the volume formula for h ...

take the derivative w/r to r and set the result equal to zero ...

sub this value into the equation where h is in terms of r ... you should see that h = 2r ; the max volume for a fixed surface area occurs when the cylinder's side profile is a square.