A sphere, a cylinder and a cone have the same radius and same height, then the ratio of their curved surface areas is

Correct option is: B) 4 : 4 : √5

Given that 

Radius of cylinder = Radius of cone = Radius of sphere = r

\(\because\) Height of the sphere = Diameter of the sphere = 2 r

\(\therefore\) Height of cylinder = Height of cone  = 2r

Now, curved surface area of sphere \(4 \pi r^2\)

curved surface are of cylinder = \(2 \pi r h\)

= 2\(\pi r (2 r) \) (\(\because\) h = 2r)

= \(4 \pi r^2\) 

curved surface area of cone = \(\pi rl\)

= \(\pi r\sqrt{r^2+h^2}\)

= \(\pi r\sqrt {r^2 + 4r^2}\) (\(\because\) h = 2r)

= \(\sqrt5 \pi r^2\)

Now, the ratio of their curved surface areas

= \((C.S.A)_S : (C.S.A)_{cylinder} : (C.S.A)_{cone}\)

= \(4 \pi r^2\) : \(4 \pi r^2\) : \(\sqrt5 \pi r^2\) 

= 4 : 4 : \(\sqrt5 \) (On dividing by \(\pi r^2\))

Hence, the ratio for their curved surface areas = 4 : 4 : \(\sqrt5 \).

Correct option is: B) 4 : 4 : √5