Q. 6

Prove that the surface area of a sphere is equal to curved surface area of the circumscribed cylinder.

Answer :

Given: Radius of sphere = Radius of cylinder = r

To Prove: surface area of sphere = curved surface area of the circumscribed cylinder

Formula Used:

The curved surface area of cylinder = 2πrh

The surface area of sphere = 4πr2


For radius “r” units,

CSA of sphere = 4πr2

The height of cylinder = Diameter of sphere

= 2×Radius of sphere

= 2×r

= 2r units

Curved surface area of cylinder = 2πr(2r)

= 4πr2

Hence proved

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