[SOLVED] Maximizing an Object 1. The problem statement, all variables and given/known data What proportions will maximize the volume of a projectile in the form of a circular cylinder with one conical end and one flat end, if the surface area is given? (there is a picture given with r being the radius, l being the length of the cylinder and s being the length of the cone(outside edge)) 2. Relevant equations 3. The attempt at a solution Well I can come up with: SA = [tex]\pi*r^2+ 2\pi*rl + \pi*rs[/tex] V = [tex]\pi*r^2l + \pi / 3r^2*s*sin\theta[/tex] I've tried both using Lagrange multipliers and just using partial derivatives. but haven't really come up with anything... (r, l, s) [tex]<2\pi rl + 2/3\pi*r*s*sin\theta, \pi r^2 + 0, 1/3\pi*r^2*sin\theta> = \lambda*(<2\pi r + 2\pi l + \pi s, 2\pi r, \pi r>[/tex] Then with using the 3 equations I was getting r = 2l and l = lamda, which isn't the case, so I think I must either need another equation or my equations are wrong?