Moon vs Earth — diameter ratio 1 : 4 — find volume ratio: The Moon’s diameter is approximately one-fourth of Earth’s diameter. What is the approximate ratio of their volumes (Moon : Earth)?

Introduction / Context:Solid volumes scale with the cube of the linear dimension. If one sphere’s diameter is a fixed fraction of another’s, their volumes are in the cube of that fraction.

Given Data / Assumptions:

• d_Moon : d_Earth = 1 : 4.
• Volumes of spheres V ∝ d^3 (equivalently r^3).

Concept / Approach:Compute (1/4)^3 = 1/64 to get Moon : Earth volume ratio.

Step-by-Step Solution:V_Moon : V_Earth = (1^3) : (4^3) = 1 : 64

Verification / Alternative check:Using radii gives the same result since radius is proportional to diameter.

Why Other Options Are Wrong:1 : 4 and 4 : 16 ignore cubic scaling; 1 : 128 would correspond to diameter ratio 1 : 5 approximately, not 1 : 4.

Common Pitfalls:Applying linear or square scaling to a volume comparison.

Final Answer:1 : 64