(Q4) A sphere, a cylinder and a cone are of the same radius and same height.Find the ratio of their curved surface areas.

Solution :

Let r be the common radius of a sphere, a cone and cylinder.

Height of sphere = its diameter = 2r.

Then, the height of the cone = height of cylinder = height of sphere = h = 2r

The slant height of cone l = √(r² + h²)

  = √(r² + ( r)² ) = √ ( ) r

S₁ = Curved Surface area of sphere = 4πr²

S₂ = Curved Surface area of cylinder, 2πrh = 2πr × r = πr²

S₃ = Curved Surface area of cone, πrl = πr × √ r = √ πr²

∴ Ratio of curved surface area is

S₁ : S₂ : S₃ = πr² : πr² : √ ( ) πr²

= : : √ ( )