A right circular cylinder and a cone are there. Base radius of cone is equal to radius of cylinder. What is the ratio of height to slant side if their volume are the same?

• 1/3 pi r^2 h1 = pi r^2 h2
  h1/h2= 3/1
  
  height of cone : height of cylinder = 3:1
• 12 years agoHelpfull: Yes(18) No(21)
• since there volume are same then :
  pi*(r)square*h=(1/3)*pi*(r)square*h which gives 1:3
• 11 years agoHelpfull: Yes(9) No(10)
• They have asked the ratio of cylinder to the cone
  so Cylinder volume is pi*r^2*h
  cone volume is 1/3*pi*r^2*l
  cylinder/cone=h/l=1/(1/3)=3/1==3:1
• 11 years agoHelpfull: Yes(4) No(12)
• cylinder=pi*r^2*h1
  cone=(1/3)*pi*r^2*h2
  pi*r^2*h1=(1/3)*pi*r^2*h2
  h1/h2=1/3
  
• 8 years agoHelpfull: Yes(3) No(2)
• pi*r^2*h1 = 1/3 *pi *r^2 *h2
  so, h1 / h2 = 1:3
• 9 years agoHelpfull: Yes(1) No(3)
• Slant height = (r^2 + h^2)^(1/2)
  h1/h2=3:1
• 10 years agoHelpfull: Yes(0) No(3)
• slant side means inclined of cone.so the ratio of height of cylinder to the slant side is
  h1=x/2*3.14*r and h2=x/3.14&r,
  h1:h2=2:1,where x is surface area because radius is equal & only height is different.so
  ans is 2:1
• 9 years agoHelpfull: Yes(0) No(1)
• cylinder=pi r^2 h1
  cone=1/3 pi r^2 h2
  h2/h1 =3 : 1
• 7 years agoHelpfull: Yes(0) No(1)
• Volume of a cylinder = (pi)r^2*h(cylinder).
  
  Volume of a cone = (1/3)(pi)r^2*h(cone).
  
  Since volumes are the same, h(cylinder)= (1/3)(cone, or
  
  h(cone) = 3h(cylinder).
  
  Slant height of cone = [r^2 + h(cone)^2]^0.5 = [1 + h(cone)^2]^0.5
  
  = [1 + {3h(cylinder)}^2]^0.5
  
  Hence, ratio of height of cylinder to slant height of cone =h(cylinder) : [1 + {3h(cylinder)}^2]^0.5 .
  
  If h(cylinder) is taken as unity, then ratio of height of cylinder to slant height of cone =1 : [1 + 3^2]^0.5 = 1:√10.
• 5 years agoHelpfull: Yes(0) No(0)