GATE AG 2017 • Q20 NAT • 1 Mark

Section 6: Agricultural Process Engineering

Engineering Properties of Agriculture Produce

Subtopic: Electrical properties

Question Statement:

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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