Multiple choice

A sphere of radius 4 cm is melted and recast into smaller spheres of radii 2 cm each. How many such spheres can be made?

  1. 4

  2. 8

  3. 32

  4. 16
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of large sphere = 4/3 * pi * 4^3. Volume of small sphere = 4/3 * pi * 2^3. Number of spheres = (4^3) / (2^3) = 64 / 8 = 8.

AI explanation

Using the formula for the volume of a sphere, the original volume is four thirds times pi times 4 cubed, which equals 256 pi over 3 cubic cm. The volume of one smaller sphere of radius 2 cm is four thirds times pi times 2 cubed, equaling 32 pi over 3 cubic cm. Dividing 256 pi over 3 by 32 pi over 3 gives 8.

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