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GATE 2025 Chemical Engineering, Q41 · Mechanical Operations

The correct answer is C, 2(r²h/2)^(2/3) / [r√(r²+h²)].

Question

A catalyst particle is modeled as a symmetrical double cone solid, as shown in the figure. For each conical sub-part, the radius of the base is r and the height is h. The sphericity of the particle is given by

Figure for Q41 (Mechanical Operations, Particle Characterization): A catalyst particle is modeled as a symmetrical double cone solid, as shown in the figure. For each…
  • A. 2(r2h/2)1/3/[rr2+h2]2(r²h/2)^{1/3} / [r\sqrt{r²+h²}]
  • B. (r2h/2)1/3/[rr2+h2](r²h/2)^{1/3} / [r\sqrt{r²+h²}]
  • C. 2(r2h/2)2/3/[rr2+h2]2(r²h/2)^{2/3} / [r\sqrt{r²+h²}]
  • D. (r2h/2)2/3/[rr2+h2](r²h/2)^{2/3} / [r\sqrt{r²+h²}]

Official answer: 2(r2h/2)2/3/[rr2+h2]2(r²h/2)^{2/3} / [r\sqrt{r²+h²}]

Why

GATE 2025 official key: (C). Sphericity is the ratio of the surface area of a sphere of equal volume to the actual surface area of the particle; for the double-cone geometry this reduces to 2(r2h2)2/3/[rr2+h2].2(r²h²)^{2/3} / [r\sqrt{r²+h²}].

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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