Multiple choice

A sphere of radius 9 cm is melted and recast into small spheres of radius 2 cm each. How many such sphere can be made?

  1. 90

  2. 92

  3. 93

  4. 91
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of large sphere = (4/3)*pi*9^3. Volume of small sphere = (4/3)*pi*2^3. Number of spheres = (9^3) / (2^3) = 729 / 8 = 91.125. Since we need whole spheres, 91 can be made.

AI explanation

When a solid is melted and recast, its total volume remains the same, calculated by the sphere volume formula V equals four-thirds times pi times the radius cubed. The volume of the large sphere is four-thirds pi times 9 cubed, which is four-thirds pi times 729, and the volume of a small sphere is four-thirds pi times 2 cubed, which is four-thirds pi times 8. Dividing the large volume by the small volume gives 729 divided by 8, which equals 91 with a remainder of 1, resulting in 91 complete spheres.

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