Show that the right circular cylinder of given surface
Question: Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base.
Solution: Let be the radius of the circular base and be the height of closed right circular cylinder.
Formula for Total surface area
Volume of cylinder
Differentiating with respect r
For max and minima
Hence volume of cylinder is max when
Value of S putting in equation (i)
Height of cylinder = Diametre of cylinder
Hence volume of cylindr is max when