Show that its volume is a maximum

[thereddevils]

Homework Statement

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 $$r=r\sqrt{2}h$$

Homework Equations

The Attempt at a Solution

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

V=1/3 pi r^2 h

 

[Rajini]

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

 

[thereddevils]

what is m?

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

 

[thereddevils]

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

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