19 Jul '11 17:29

Is there optimal dimensions such that a cylinder can have maximum surface area for any fixed volume?

Here's what I started, but I come to something that might be considered a nonphysical result...I could be making a logical error as a kinda just conjured this up

starting with the equation for volume

V = pi*r^2*h

If the two parameters r & h were to be varied, and the volume was to remain constant it would imply ( or so i think)

V_r(h,r) + V_h(h,r) = 0

2*pi*h*r + pi*r^2 = 0

which then follows

h= -1/2*r

which isn't possible...

As i said, im now not sure any of this makes sense.

Here's what I started, but I come to something that might be considered a nonphysical result...I could be making a logical error as a kinda just conjured this up

starting with the equation for volume

V = pi*r^2*h

If the two parameters r & h were to be varied, and the volume was to remain constant it would imply ( or so i think)

V_r(h,r) + V_h(h,r) = 0

2*pi*h*r + pi*r^2 = 0

which then follows

h= -1/2*r

which isn't possible...

As i said, im now not sure any of this makes sense.