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Q25 (CISF/2026) Science & Technology › Basic Science (Physics, Chemistry, Biology)

Ten identical silver coins are melted to make new coins having half the thickness and one-third the diameter of the original coins. What is the total number of new coins made ?

Result
Your answer: —  ·  Correct: D

Explanation

This problem is solved using the principle of conservation of volume. A coin is a cylinder, and its volume is calculated as V = πr²h (where r is radius and h is thickness).

  • Let the original radius be R and thickness be H. The total volume of 10 coins is 10 × πR²H.
  • The new coins have one-third the diameter, meaning the new radius r = R/3. The new thickness h = H/2.
  • The volume of one new coin = π × (R/3)² × (H/2) = π × (R²/9) × (H/2) = πR²H / 18.
  • To find the total number of new coins (n), we divide the total original volume by the volume of one new coin: n = (10 × πR²H) / (πR²H / 18).
  • This simplifies to n = 10 × 18 = 180.

Therefore, 180 new coins can be made.

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