Surface Areas and Volumes — Question 13

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.