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

1 : 1

The cylinder that circumscribing the sphere perfectly will be of equal radius and height of cylinder will be equal to diameter of sphere.

Therefore,

⇒ Surface area of sphere = 4\(\pi \)r²

⇒ C.S.A. of the cylinder = 2\(\pi \)rh = 2\(\pi \)r × 2r = 4\(\pi \)r²

⇒ Ratio = 1 : 1