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Question

A right circular cylinder just encloses a sphere of radius r. Find ratio of the surface area of the sphere and curved surface area of the cylinder.
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Solution

Given that the cylinder just encloses a sphere of radius r.
Hence, radius of the cylinder = radius of the sphere =r
and height of the cylinder = diameter of the sphere =2r
To find: Ratio of the surface area of sphere and curved surface area of cylinder.
We know that,
Surface area of sphere =4πr2
and C.S.A. of cylinder =2πrh

Required ratio =4πr22πrh

4πr22πr(2r) [h=2r]

4πr24πr2=11

Hence, the ratio of the surface area of the sphere and the curved surface area of the cylinder is 1:1.

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