A sphere is melted and molded into a solid cylinder. If the radius of both solids is equal, then find the ratio of the total surface area of the sphere to the total surface area of the cylinder.
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$2 : 3$
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$4 : 3$
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$3 : 7$
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$6 : 7$
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$7 : 6$
D
Correct answer
Explanation
Sphere volume = (4/3)πr³ = cylinder volume = πr²h. Height h = 4r/3. Sphere surface area = 4πr². Cylinder surface area = 2πr² + 2πrh = 2πr² + 2πr(4r/3) = 2πr² + 8πr²/3 = 14πr²/3. Ratio = 4πr² : 14πr²/3 = 4 : 14/3 = 12 : 14 = 6 : 7. Option D is correct.