For a perfect sphere, which formula gives the volume shape factor in terms of diameter D and volume V (identify the standard expression)?

Introduction / Context:
Shape factors relate geometric measures like volume V, surface area A, and a characteristic size D. For spheres, simple constants appear that are frequently used in particle technology problems.

Given Data / Assumptions:

• Sphere of diameter D.
• Volume of sphere V = (π/6) * D^3.
• Surface area A = π * D^2.

Concept / Approach:
The volume of a sphere expressed with diameter instead of radius yields V = (π/6) * D^3. Rearranging, V / D^3 = π/6, the classic volume shape factor for spheres. This identity underpins many sizing and normalisation relationships in particle science.

Step-by-Step Solution:
Recall V_sphere = (4/3)πr^3 and D = 2r.Substitute r = D/2 to get V = (π/6) D^3.Identify the required expression π/6 = V / D^3.

Verification / Alternative check:
Cross-check with A = π D^2 for spheres to ensure dimensional consistency of related shape factors.

Why Other Options Are Wrong:
A/D^2 and 2A/D^2 relate to area-based factors, not volume shape factor.A D / V is not a constant for spheres.6/π = D^3 / V is a rearranged equivalent but not the canonical expression as asked.

Common Pitfalls:
Mixing radius and diameter, leading to incorrect constants.

Final Answer:
π/6 = V / D^3