Question 1084213
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1.  Let "r" be the radius of the sphere.

    Since the sphere is inscribed in the cylinder, the radius of the cylinder is "r" too, and the height of the cylinder is h = 2r.


2.  Surface area of the sphere is {{{S[sphere]}}} = {{{4*pi*r}}}.


3.  Lateral surface area of the cylinder is {{{S[cylinder]}}} = {{{2*pir*h}}} = {{{2*pi*r*(2*r)}}} = {{{4*pi*r^2}}}.


4.  Comparing these expressions, we can conclude that in the considered case 


            <U>the surface area of the sphere is equal to the lateral area of the cylinder</U>.
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Solved.