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Question

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


Solution

Sol:
Let the radius of the sphere = r
Surface area of the sphere = 4πr2
Radius of the cylinder circumscribed over the sphere = r
Height of the cylinder circumscribed over the sphere (h) = 2r
Curved surface area of the cylinder = 2πrh
                                                   = 2πr(2r)
                                                   = 4πr2
Therefore, the curved surface area of the circumscribed cylinder over a sphere is equal to the surface area of the sphere.


Mathematics
RD Sharma
Standard X

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