Multiple choice

A solid metal sphere of surface area $S_1$ is melted and recast into a number of smaller spheres. $S_2$ is the sum of the surface areas of all the smaller spheres. Then.

  1. $S_1 > S_2$
  2. $S_2 > S_1$
  3. $S_1 = S_2$
  4. $S_1 = S_2$ only if all the smaller spheres of equal radii
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume is conserved, but surface area increases when a large sphere is broken into smaller ones. For a fixed volume, the sphere has the minimum surface area. Thus, S2 > S1.

AI explanation

When a solid sphere is melted and recast into multiple smaller spheres, the total volume remains unchanged, but the total surface area increases. This occurs because breaking a shape into smaller pieces increases its collective surface area. Therefore, the sum of the surface areas of all the smaller spheres will be greater than the surface area of the original sphere.

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