Question

a cylinder and a cone are of the same radius and same height.express ratio of their curved surface areas

Answer 1

Number of Curve Surface in Cylinder=2
Number of Curved Surface in Cone=1
(And else everything is equal)
Hence,the ratio of their curved surfaces is (2:1)

Answer 2

The height of a sphere is the diameter, the cone have height 2r. 

Then 
Curved surface area of Sphere= 4πr²

Curved surface area of cone = πrl

where, l = √(r^2 + h^2 ) = √( r^2 + (2r)^2) = √(5r^2) = r√5  

⇒ Curved surface area of cone = π√5r^2 

Ratio of CSA 's a sphere and a cone = 4πr2:πrl

= 4πr^2:πr^2√5

= 4 :√5