Q15 of 51 Page 1

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

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


Explanation:


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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