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

Answer: Option A

Let the radius of the sphere be r
Then, radius of the cylinder = r
Height of the cylinder = 2r
Surface area of sphere = $$4\pi {\text{r}}^2$$
Surface area of the cylinder = $$2\pi \text{r}(2r)=4\pi {\text{r}}^2$$
∴ Required ratio :
= $$4\pi {\text{r}}^2$$ : $$4\pi {\text{r}}^2$$
= 1 : 1