hello,
please guys i need your help for this problem as part of my final preparation:
Use the arithmetic-geometric mean inequality to find the radius of a cylinder with
prescribed surface area and the largest possible volume.
Hints: The volume and the surface area of a cylinder of height h and radius r are given
use V = Pi*h*r^2 and S = 2*pi*r^2 + 2*pi*r*h, respectively. Eliminate h.
i tried doing that but all i could do is use calculus and calculated V in function of S and r, and put that V is maximum means that V' = 0 and calculated r in function of S.
i found r= cubic root of (-S/3*pi)
is there any way to do this using arithmetic geometric mean?!
thank you very much!
please guys i need your help for this problem as part of my final preparation:
Use the arithmetic-geometric mean inequality to find the radius of a cylinder with
prescribed surface area and the largest possible volume.
Hints: The volume and the surface area of a cylinder of height h and radius r are given
use V = Pi*h*r^2 and S = 2*pi*r^2 + 2*pi*r*h, respectively. Eliminate h.
i tried doing that but all i could do is use calculus and calculated V in function of S and r, and put that V is maximum means that V' = 0 and calculated r in function of S.
i found r= cubic root of (-S/3*pi)
is there any way to do this using arithmetic geometric mean?!
thank you very much!