Show that the right circular cylinder, open at the top, and of given surface area and maximum volume is such that its height is equal to the radius of the base.

Explanation

Let r be the radius and h be the height of the cylinder of given surface s. Then,


`s=pi r^{2}+2 pi h r `
`
h=frac{s-pi r^{2}}{2 pi r}`


Then
`
v=pi r^{2} h=pi r^{2}[frac{s-pi r^{2}}{2 pi r}] `[ From eqn. (i)]


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