Thread: Optimization of cylinder

A cylinder has volume of 10m^3. What are the dimensions that will give the maximum & minimum surface areas. (if there is no max or min state why)

I think I need to make a function for surface area, use max & min of the deriv perhaps?

not sure how to turn this into deminsions

EDIT:
So for a first step I solved volume equation for H and then do I put that back into my surface area equation?

I ended up with a radius= 1.16 and h=2.33 does this sound reasonable?

I did S'(r)=0 for r and then used that to solve for my h.

Originally Posted by mattc

I ended up with a radius= 1.16 and h=2.33 does this sound reasonable?

I did S'(r)=0 for r and then used that to solve for my h.

for min surface area, h = 2r

no max

oh good.

I also came to the conclusion that there is no max because S'' is always positive/concave up so in critical value is a min. ...I think? yeah? lol