text: # ap Calculus
  
  posted by 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 - ,
  
  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!
  
  • ap Calculus - ,
  
  I am sure that Dr Russ meant to type
  
  volume of cone is
  
  V=1/3(pi)r^2h
  
  • ap Calculus - ,
  
  Yes oops!
  
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