A right circular cylinder just encloses a sphere of radius r (see Fig). Find
i) surface area of the sphere
ii) curved surface area of the cylinder
iii) ratio of the areas obtained in i) and ii).

i) Surface area of sphere = \(4 {\pi} {r}^2\)

ii) Height of cylinder = r + r = 2r
Radius of cylinder = r
We know that,

CSA of cylinder
= \(2{\pi}rh\)
= \(2{\pi}r(2h)\)
= \(4{\pi} {r}^2\)


iii) ratio of the areas obtained
= \(\frac{Surface area of sphere}{CSA of cylinder}\)
= \(\frac{4 {\pi} {r}^2}{4 {\pi} {r}^2}\)
= \(\frac{1}{1}\)

Therefore, the ratio between these two surface areas is 1:1.