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Question
A right circular cylinder just encloses a sphere of radius r (see figure). Find
- surface area of the sphere,
- curved surface area of the cylinder,
- ratio of the areas obtained in (i) and (ii).
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Solution
(i) Surface area of sphere = 4πr2
(ii) Height of cylinder = r + r = 2r
The radius of the cylinder = r
The curved surface area of cylinder = 2πrh
= 2πr (2r)
= 4πr2
(iii) Required ratio = `"Surface area of the sphere"/"Curved surface area of cylinder"`
= `(4pir^2)/(4pir^2)= 1/1`
Therefore, the ratio between these two surface areas is 1 : 1.
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