Multiple choice general knowledge math & puzzles

My Dad has a miniature Pyramid of Egypt. It is 4 inches in height. Dad was invited to display it at an exhibition. Dad felt it was too small and decided to build a scaled-up model of the Pyramid out of material whose density is (1 / 2) times the density of the material used for the miniature. He did a "back-of-the-envelope" calculation to check whether the model would be big enough. If the mass (or weight) of the miniature and the scaled-up model are to be the same, how many inches in height will be the scaled-up Pyramid? Give your answer to two places of decimal.

  1. 5.04

  2. 4.05

  3. 4.25

  4. 4.55

  5. 5.25
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A Correct answer
Explanation

Mass = Volume × Density. For similar pyramids, Volume ∝ height³. If mass is constant and density halves, Volume must double. So height³ becomes 2 times original. New height = 4 × 2^(1/3) = 4 × 1.26 = 5.04 inches (to two decimals).

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