Answer Posted / Om Pal Singh

Let r be the radius of the sphere and h be the height of the cylinder. The radius of the base of the cylinder is also r. Since the sphere circumscribes the cylinder, its diameter is equal to the diameter of the base of the cylinder, so 2r = 2 * (radius of the base) = 2 * r. Therefore, r = r. Now, the surface area of the sphere is 4πr². The curved surface area of the cylinder is 2πrh. Since the volume of the sphere is equal to the volume of the cylinder (both are circumscribed by the same sphere), we have 4/3 * πr³ = πr²h. Solving for h, we get h = 4/3 * r. Now, the ratio of the surface area of the sphere to the curved surface area of the cylinder is 4πr² / (2πrh) = (2r)/(3h). Substituting h = 4/3 * r, we find the ratio is (2r) / (3 * (4/3 * r)) = 2 : 1.

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