A cylinder and a cone have equal radii of
their bases and equal heights. If their
curved surface areas are in the ratio 8 : 5,
the ratio of their radius and height is

• Let R be the radius, h be height.
  
  CSA of cone = π(Radius)(Slant Height) = πR((R2+h2))
  
  CSA of cylinder = 2π(Radius)(Height) = 2πRh
  
  CSA of cone/CSA of cylinder = 5/8 = [πR((R2+h2))]/(2πRh)
  
  ((R2+h2))/(2h) = 5/8
  
  Squaring on both sides,
  
  (R2+h2)/(4h2) = 25/64
  
  (R2+h2)/h2 = 100/64
  
  R2/h2 + 1 = 100/64
  
  R2/h2 = 100/64 - 1
  
  R2/h2 = 36/64
  
  R/h = 6/8 = 3/4
  ans 3 : 4
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