A sphere of diameter ' x ' and right circular cylinder of heights ' x ' and right circular cone of height ' x ' are of equal volume . The radii are in the ratio ?

• Sqrt(3) : Sqrt(2) : Sqrt(6)
  
  Diameter of Sphere=x, so Radius=x/2, Volume of Sphere=(4/3)*Pi*(x/2)^3=Pi*x^3/6 ---(i)
  If radius of cylinder=r1, then Volume of cylinder=Pi*r1^2*h=Pi*r1^2*x ---(ii)
  If radius of cone=r2, then Volume of cone=(1/3)*Pi*r2^2*h=(1/3)*Pi*r2^2*x=Pi*r2^2*x/3 ---(iii)
  
  As Volumes of all the three are same, comparing (i) =(ii) =(iii)
  So ,Pi*x^3/6= Pi*r1^2*x = Pi*r2^2*x/3
  r1=x/Sqrt(6) and r2=x/Sqrt(2)
  Hence Ratio of radii are (x/2) : [x/Sqrt(6)] : [x/Sqrt(2)] = Sqrt(3) : Sqrt(2) : Sqrt(6)
• 8 years agoHelpfull: Yes(2) No(0)