A right circular cylinder just encloses a sphere of radius `r` as shown in figure. Find the : 1.surface area of the sphere 2. curved surface area of the cylinder 3. ratio of the area 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`