Question

A right circular cylinder just encloses a sphere of radius r (see given 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).

Answer 1

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

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

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

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