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

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

Correct answer: 1 : 3

Solution

Conserving volume gives each small radius = 15/3 = 5 cm. Original surface area is 900pi and total of 27 small spheres is 27 x 100pi = 2700pi, so the ratio is 900:2700 = 1:3.

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