Cone of base radius 1m, height 6m. What is the maximum volume of cylinder can be formed by this cone.

• Let the radius of cylinder=x;height of cylinder=h;
  y is the length from vertex of the cone to the top surface of the cylinder
  y/x=6/1;
  Volume of cylinder=pi*x^2*h;
  h=6-(6*x);
  Volume=pi*x^2*(6-(6*x))
  Now to get the maximum volume we have to differentiate Volume with respect to x
  6*pi[2x-3x^2]=0;
  x=2/3;
  Therefore h=6-6*2/3;
  h=2;
  Volume=pi*(2/3)^2*2;
  Volume=8pi/9;
  
• 9 years agoHelpfull: Yes(14) No(1)
• Let the radius of cylinder=x;height of cylinder=h;
  y is the length from vertex of the cone to the top surface of the cylinder
  y/x=6/1;
  Volume of cylinder=pi*x^2*h;
  h=6-(6*x);
  Volume=pi*x^2*(6-(6*x))
  Now to get the maximum volume we have to differentiate Volume with respect to x
  6*pi[2x-3x^2]=0;
  x=2/3;
  Therefore h=6-6*2/3;
  h=2;
  Volume=pi*(2/3)^2*2;
  Volume=8pi/9;
  
  You can also check it here
  http://www.mathalino.com/reviewer/differential-calculus/cylinder-maximum-volume-and-maximum-lateral-area-inscribed-cone
• 9 years agoHelpfull: Yes(7) No(0)
• ans: 2 pie
• 9 years agoHelpfull: Yes(5) No(7)
• 6pie , Because volume of cylinder pie*r^2*h
• 9 years agoHelpfull: Yes(0) No(5)
• ans is 9pie/4
  cylinder will reach its max volume when the height of cylinder will be half of the height of cone....if we consider that,we will be able to see the radius of cylinder becoming half of the radius of cone....volume of cylinder will be pie*1/2*1/2*3
• 9 years agoHelpfull: Yes(0) No(2)
• 1-h/1 = r/6 h = hight of cylinder , r = radius of cone.(using ~ triangle concept)
  
  h = 1-r/6
  
  dV/dr=0, v= 1/3*pi*r^2*(1-r/6) (V of cone)
  r=4 , h= 1/3.
  
  then volume of cyl. = pi*r^2*h = Pi*16/3.
• 9 years agoHelpfull: Yes(0) No(1)
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• 9 years agoHelpfull: Yes(0) No(0)
• How do we valuate h=6-(6*x);
• 9 years agoHelpfull: Yes(0) No(0)