Question

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

Answer 1

SOLUTION :

Let the radius of the sphere be (r)

Surface area of the sphere , S1 = 4πr² ………….. (1)

Radius of the cylinder = radius of the sphere = r

Height of the cylinder = diameter of a sphere =  2r

Curved surface area of the cylinder = 2πrh

S2 = 2πr (2r) = 4πr² ……………..(2)

From equation 1 & 2 , it is prove that surface area of the sphere is equal to the curved surface area of the circumscribed cylinder.

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Answer 2

Sol: Let the radius of the sphere = rSurface area of the sphere = 4πr2 Radius of the cylinder circumscribed over the sphere = r Height of the cylinder circumscribed over the sphere (h) = 2rCurved surface area of the cylinder = 2πrh                                                   = 2πr(2r)                                                   = 4πr2Therefore, the curved surface area of the circumscribed cylinder over a sphere is equal to the surface area of the sphere...

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