Question:

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

Updated On: Nov 17, 2023
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Solution and Explanation

(i) Surface area of sphere = 4πr24\pi r^2


(ii) Height of cylinder = r + r = 2r 
Radius of cylinder = r
CSA of cylinder = 2πrh=2πr(2r)2\pi rh = 2\pi r (2r)
= 4πr2= 4\pi r^2


(iii) The ratio of the areas obtained in (i) and (ii) is:

4πr24πr2 =11\frac{4\pi r^2}{4\pi r^2} = \frac{1}{1}
Therefore, the ratio between these two surface areas is 1:1.

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