# Homework Help: Show that its volume is a maximum

1. Apr 28, 2010

### thereddevils

1. The problem statement, all variables and given/known data

A right circular cone has base radius , r and height h . As r and h vary its curved surface area is kept constant . Show that its volume is a maximum when $$r=r\sqrt{2}h$$

2. Relevant equations

3. The attempt at a solution

A= pi r^2 + pi r root(r^2+h^2)

V=1/3 pi r^2 h

Last edited: Apr 28, 2010
2. Apr 28, 2010

### Rajini

Re: differentiation

what is m?
$$r=r\sqrt{2}h$$
means: $$1=h\sqrt{2}$$ ? and h=0.707 ?

Last edited: Apr 28, 2010
3. Apr 28, 2010

### thereddevils

Re: differentiation

Its a typo , the m shouldn't be there . Edited

4. Apr 28, 2010

### thereddevils

Re: differentiation

thats what confuses me , i am not sure whether thats a typo in the book , i need someone to confirm that for me . What do you think ?