Posted by Corey on Wednesday, November 5, 2008 at 10:38am.
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!
I am sure that Dr Russ meant to type
volume of cone is
V=1/3(pi)r^2h
Yes oops!
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