The ratio of the surface area of a sphere and the curved surface area of the cylinder circumscribing the sphere is:

Question: The ratio of the surface area of a sphere and the curved surface area of the cylinder circumscribing the sphere is:

Solution:
Let the radius of the sphere be r
Then, the radius of the cylinder = r
Height of the cylinder = 2r
Surface area of sphere = 4πr²

Surface area of the cylinder = 2πr(2r) = 4πr²

∴ Required ratio
= 4πr² : 4πr²
= 1 : 1