A cylindrical (right circular cylinder) package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 108 inches. Find the dimensions of the package of maximum volume that can be sent. (assume the cross section is circular)

Question

anonymous · Answer

I got V = 2916 in^3

cwrw238 · Answer

L + 2pi R = 108

V =  pi R^2 L

substituting in V for L

V = piR^2 (108 - 2Pi R)

find dV / dR  and equate to 0 to find R for maxm V 

is that the way you did it?

anonymous · Answer

Yes, precisely! I'm just not sure if my answer is right.

cwrw238 · Answer

dV/dR = 216piR - 6pi^2 R^2 = 0
6piR (piR - 36) = 0
R = 36 / pi = 11.459 

so
L = 108 - 2 pi * 11.459 = 36.001

V =  pi * 11.459^2 * 36.001 = 14851

if my calculations are correct!!

anonymous · Answer

Ah, okay. I think I messed up on the derivative part.

cwrw238 · Answer

i've checked it out and cant find anything wrong

anonymous · Answer

So pi just stays as is when you take a derivative?

cwrw238 · Answer

yea pi is  a constant

anonymous · Answer

Blubber nuggets! Okay. Thanks!

cwrw238 · Answer

lol  - yw