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Question:

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

Solution:

(i) SA of sphere = 4πr²
(ii) Height = r + r = 2r
radius = r ⇒ Curved Surface Area = 2πrh = 2πr(2r) = 4πr²
(iii) Ratio = 4πr²/4πr² = 1/1 or 1:1