Posted by Corey on .
A right circular cone has a fixed slant height, s= 12 inches. Determine the radius and the height of the cone with maximum volume

ap Calculus 
Dr Russ,
volume of cone is
V=4/3(pi)r^2h
s^2=r^2+h^2 or s^2h^2=r^2
V=4/3(pi)(s^2h^2)h
if 4/3(pi)=k
V=k(144h^2)h
V=144khkh^3
volume is a max when dV/dh is zero
dV/dh = 144k3kh^2
144k3kh^2 = 0
144k = 3kh^2
48=h^2
this gives you h, from which you can find r from
s^2h^2=r^2
please check my maths! 
ap Calculus 
Reiny,
I am sure that Dr Russ meant to type
volume of cone is
V=1/3(pi)r^2h 
ap Calculus 
Dr Russ,
Yes oops!