A solid rightcircular cone has a radius of 6cm and height 1cm. what is the maximum possible volume of a solid cylinder cut from that cone?

• Express the height in terms of the radius.
  Since h=1, r=6
  
  h = (1 – r/6)
  
  V = πr²h
  V = πr²(1 – r/6)
  V = πr² - πr³/6
  dV/dr = 2πr - (3/6)πr²
  
  Let dV/dr = 0
  2πr - (1/2)πr² = 0
  2r –(1/2) r² = 0
  r = 0 &,
  r = 4 ............... Reject r = 0.
  
  V = πr²(1 – r/6)
  V = 16π/3 cm³
  
• 11 years agoHelpfull: Yes(32) No(4)
• the formula to find the highest possible volume of a cylinder inscribed inside a cone is V = pi*(r^2)*h*(4/27)
  so r=6 and h=1
  therfore V= pi*(6*6)*1*(4/27)=(16/3)*pi
• 11 years agoHelpfull: Yes(18) No(0)
• @mohit h=(1-r/6)=0, r=6
• 11 years agoHelpfull: Yes(6) No(1)
• I am moving this to calculus since it is more of a calc problem.
  
  Let R and H be the radius and height of the cone, and r and h be the radius and height of the cylinder.
  
  The volume of the cylinder is V={pi}r^{2}h
  
  Now, as in a lot of these problems, use similar triangles.
  
  frac{H-h}{H}=frac{r}{R}
  
  Therefore, h=frac{H}{R}(R-r)
  
  Plug this into the cylinder volume equation at the top. H and R are given constants.
  
  Then differentiate to find dV/dr. Set to 0 and solve for r.
  
  If done correctly, you should find that the volume of the cylinder that has max volume is 4/9 the volume of the cone.
• 11 years agoHelpfull: Yes(2) No(3)
• @awasthi... kahn s mila yar y...solution ?
• 11 years agoHelpfull: Yes(1) No(6)