Multiple choice

How many spheres of iron having radius $1cm$ can be made by melting a sphere of iron having $8cm$ radius?

  1. $64$
  2. $128$
  3. $356$
  4. $512$
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D Correct answer
Explanation

Volume of large sphere = (4/3) * pi * 8^3. Volume of small sphere = (4/3) * pi * 1^3. Number of spheres = 8^3 / 1^3 = 512.

AI explanation

The volume of a sphere is given by the formula V = (4/3)πr^3, so the large sphere has a volume of (4/3)π(8)^3 and each small sphere has a volume of (4/3)π(1)^3. To find the number of small spheres, divide the large volume by the small volume to get 8^3 / 1^3. Calculating 512 divided by 1 results in 512 spheres.

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