Question

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

Answer 1

volume of cone is

V=4/3(pi)r^2h

s^2=r^2+h^2 or s^2-h^2=r^2

V=4/3(pi)(s^2-h^2)h

if 4/3(pi)=k

V=k(144-h^2)h

V=144kh-kh^3

volume is a max when dV/dh is zero

dV/dh = 144k-3kh^2

144k-3kh^2 = 0

144k = 3kh^2
48=h^2

this gives you h, from which you can find r from

s^2-h^2=r^2

please check my maths!

Answer 2

I am sure that Dr Russ meant to type

volume of cone is

V=1/3(pi)r^2h

Answer 3

Yes oops!