Multiple choice

A sphere of radius 6 cm is melted and recast into spheres of radius 2 cm each. How many such spheres can be made?

  1. 36

  2. 25

  3. 27

  4. 24
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C Correct answer
Explanation

The volume of a sphere is given by (4/3) * pi * r^3. The volume of the large sphere is (4/3) * pi * 6^3, and the volume of each small sphere is (4/3) * pi * 2^3. Dividing the large volume by the small volume gives (6/2)^3 = 3^3 = 27.

AI explanation

Because the volume is conserved when the large sphere is melted and recast, the number of smaller spheres is the volume of the large sphere divided by the volume of one small sphere, written as ((4 / 3) * pi * R^3) divided by ((4 / 3) * pi * r^3). This simplifies to (R / r)^3, and substituting the radii of 6 cm and 2 cm gives (6 / 2)^3, which is 3^3. Evaluating this results in 27 spheres.

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