Sphericity of a cube with each side as L is __________.
Official Answer Key:
0.707 to 0.807
Step-by-Step Solution & Explanation
• Sphericity, φ = (surface area of a sphere having the same volume as the particle) / (actual surface area of the particle).
• Cube volume = L³. Equivalent-volume sphere diameter de: (π/6)de³ = L³ ⇒ de = L(6/π)^(1/3).
• Sphere surface area = πde² = πL²(6/π)^(2/3). Cube surface area = 6L².
• φ = π(6/π)^(2/3)/6. Numerically, (6/π)=1.9099, raised to 2/3 ≈ 1.539; φ = π×1.539/6 ≈ 4.834/6 ≈ 0.806, inside the accepted range 0.707–0.807.
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