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

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Solution

We have the following figure to visualize the situation

Let the radius of the sphere is r. Therefore, the surface area of the sphere is

The circumscribed cylinder of the sphere must have radius r cm and height 2r cm. Therefore, the curved surface area of the cylinder is

Hence, S and S₁ are same. Thus the proof is complete.

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