Given, A sphere, a cylinder and a cone are in the same radius and same height.

Let radius = r

and, height = h

Height of cylinder = Height of cone = Height of sphere = Diameter of sphere = 2r

Hope it helps :)

1

Ruchir Padhye answered this

let the radius be r. Let the height by h.
The height of a sphere is the diameter = 2r

For sphere CSA = 4πr^{2}
For cylinder CSA = 2πrh = 2πr(2r) = 4πr^{2}
For cone CSA = πr x sqrt(r^{2} + h^{2}) = πr x sqrt(r^{2} + (2r)^{2}) = πr x sqrt(5r^{2}) = πr x r x sqrt(5) = πr^{2}sqrt(5)

From these 3, you get:
4πr^{2 }: 4πr^{2} : πr^{2}sqrt(5)
= 4 : 4 : sqrt(5)