Sphericity (phi) is defined as the surface area of a volume-equivalent sphere divided by the actual particle surface area. Which shape has the maximum possible sphericity?

Introduction / Context:
Sphericity is used to characterise particle shape effects on drag, packing, and surface-area-dependent phenomena. It normalises shapes against a perfect sphere with the same volume.

Given Data / Assumptions:

• Sphericity phi = (surface area of volume-equivalent sphere) / (actual surface area).
• 0 < phi ≤ 1 by definition.

Concept / Approach:
The sphere minimises surface area for a given volume. Therefore, the numerator and denominator become equal only for a sphere, giving phi = 1. All other shapes have larger surface areas for the same volume, producing phi < 1.

Step-by-Step Solution:
Recall isoperimetric principle: sphere minimises area for fixed volume.Thus the ratio reaches its maximum (1) for a sphere.Select sphere as the answer.

Verification / Alternative check:
Empirical shape factors confirm cubes, cylinders, and engineered packings have phi significantly less than 1.

Why Other Options Are Wrong:
Cube/Cylinder: greater surface area per unit volume.Raschig rings: deliberately non-spherical, very low sphericity.

Common Pitfalls:
Confusing roundness (edge smoothness) with sphericity (global shape metric).

Final Answer:
Sphere