A right circular cylinder just encloses a sphere of radius r (see Fig. 13.22). Find (i) surface area of the sphere, (ii) curved surface area of the cylinder, (iii) ratio of the areas obtained in (i) and (ii).

Explanation

The radius of the sphere = r
Radius of the cylinder = radius of the sphere = r
Height of the cylinder = diameter = 2r
(i) Surface area of the sphere `A_(1)=4pi r^(2)`
(ii) Curved surface of the cylinder `= 2pi rh`
`A_(2)=2pi xx r xx 2r`
`A_(2)=4pi r^(2)`
(iii) Required ratio `= A_(1) : A_(2) = 4pi r^(2) : 4 pi r^(2) = 1 : 1`