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GATE 2026 BM – Question 32

Biomaterials and Tissue Engineering · Biomaterial Properties · 1 mark · Numerical answer

A hollow spherical nanoparticle has outer radius 5 nm and uniform shell thickness 3 nm. Find shell volume divided by hollow-core volume, to one decimal place.

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Correct answer: 14.0 to 15.0

Explanation

Inner radius is 5−3=2 nm. Shell volume is (4π/3)(5³−2³), while core volume is (4π/3)2³. The common factor cancels, giving (125−8)/8=117/8=14.625. Rounded to one decimal place this is 14.6.

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