Multiple choice general knowledge math & puzzles

A spherical block of metal weighs 12 pounds. What is the weight, in pounds, of another block of the same metal if its radius is 3 times the radius of the 12-pound block?

  1. 324

  2. 15

  3. 108

  4. 36

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A Correct answer
Explanation

Weight scales with volume, and volume of a sphere is proportional to the cube of its radius. If the radius is multiplied by 3, the volume increases by 3^3 = 27 times. Therefore, a 12-pound block would weigh 12 × 27 = 324 pounds with 3 times the radius.

AI explanation

The weight of a sphere scales with its volume, and volume scales with the cube of the radius. Tripling the radius multiplies the volume (and hence weight) by 3^3 = 27, so 12 * 27 = 324 pounds.