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A sphere of radius “r” is fitted in a cylinder of height “h” such that the top of the sphere reaches only half the height of cylinder as shown in the figure. What is the ratio of curved surface area of a cylinder to surface area of a sphere?(a) \(\sqrt{2}\):1(b) 4:1(c) 2:1(d) 1:2I got this question in an online quiz.Question is taken from Surface Area of a Sphere in section Surface Areas and Volumes of Mathematics – Class 9

Answer»

The correct answer is (c) 2:1

Explanation: It can be SEEN that h = 4r … (1)

We know that curved surface AREA of a cylinder = 2πrh

And surface area of a sphere = 4πr^2

(We know that curved surface area of a cylinder)/(And surface area of a sphere) = 2πrh/(4πr^2)

= \(\FRAC{2πr(4r)}{4πr^2}\) (From RESULT (1))

= \(\frac{2πrh}{4πr^2}\)

= 2/1.


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