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Q104 (CGS/2026) Science & Technology › Basic Science (Physics, Chemistry, Biology)

The diameter of a sphere and the side of a cube are of equal length. Which one of the following is the correct ratio of their mass if both of them are made of the same material?

Result
Your answer: —  ·  Correct: A

Explanation

The mass of an object is given by the formula: Mass = Density × Volume. Since both the sphere and the cube are made of the same material, their density (ρ) is identical. Therefore, the ratio of their masses is equal to the ratio of their volumes.

Let the diameter of the sphere be d and the side of the cube be a. According to the question, d = a.

  • Volume of the sphere (Vs) = 4⁄3 π r3. Since radius r = d/2, Vs = 4⁄3 π (d/2)3 = 4⁄3 π (d3/8) = πd3/6.
  • Volume of the cube (Vc) = a3. Since a = d, Vc = d3.

The ratio of their masses (Ms/Mc) = (ρ × Vs) / (ρ × Vc) = Vs / Vc = (πd3/6) / d3 = π/6.

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