Sphericity of a particle is defined as: (surface to volume ratio for a sphere having identical volume as that of the particle) / (the surface to volume ratio of the particle). The measure of sphericity of a cube shaped sugar crystal is
Options:
(A) (π/6)^(1/3)
(B) (π/6)^(2/3)
(C) (π/4)^(1/3)
(D) (π/4)^(2/3)
Official Answer Key:
A
Step-by-Step Solution & Explanation
For a cube of side a: volume Vp = a³, surface area Sp = 6a², so Sp/Vp = 6/a. For a sphere of the same volume a³, its radius r = (3a³/4π)^(1/3), giving surface-to-volume ratio S_sphere/V_sphere = 3/r = 3/(3a³/4π)^(1/3). Sphericity = (S_sphere/V_sphere)/(Sp/Vp). Working this out algebraically simplifies to (π/6)^(1/3) ≈ 0.806, matching option (A) — the well-known textbook value for the sphericity of a cube.
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