A right circular cylinder just encloses a sphere of radius r. Find

(i) surface area of the sphere,

(ii) curved surface area of the cylinder,

(iii) ratio of the areas obtained in (i) and (ii).

From figure,

Radius of cylinder = radius of sphere = r

Height of cylinder = Diameter of sphere = 2r

(i) By formula,

Surface area of sphere = 4πr²

Hence, surface area of sphere = 4πr².

(ii) By formula,

Curved surface area of cylinder = 2πrh

= 2πr × 2r

= 4πr².

Hence, curved surface area of cylinder = 4πr².

(iii) Ratio = $\dfrac{\text{Surface area of sphere}}{\text{C.S.A. of cylinder}} = \dfrac{4πr^2}{4πr^2} = \dfrac{1}{1}$.

Hence, the ratio between these two surface area is 1 : 1.