A right circular cylinder just encloses a sphere of radius *r* (see figure). Find

(i) surface area of the sphere,

(ii) curved surface area of the cylinder,

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

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#### Solution

(i) Surface area of sphere = 4π*r*^{2}

(ii) Height of cylinder = *r* + *r* = 2*r*

Radius of cylinder = *r*

CSA of cylinder = 2π*rh*

= 2π*r *(2*r*)

= 4π*r*^{2}

(iii)

`"Required ratio "="Surface area of sphere"/"CSA of cylinder"`

`= (4pir^2)/(4pir^2)= 1/1`

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

Concept: Surface Area of a Sphere

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