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A solid metal sphere of radius 15 cm is melted and recast into 27 identical smaller spheres. What is the ratio of the surface area of the original sphere to the total surface area of all 27 smaller spheres?

1. 1: 3
2. 1: 6
3. 1: 9
4. 1: 15

Correct answer: 1: 3

Solution

Since volume is conserved, 27 smaller spheres each have radius \(15/3=5\) cm. Surface area is proportional to the square of radius, so each smaller sphere has \(1/9\) the surface area of the original; for 27 spheres, total surface area becomes 3 times the original.

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