Model a rod-shaped bacterium as a cylinder of radius and straight length

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Physical foundations of the living cell · Physical foundations of the living cell

Life at Thermal Energy, Ch The scales of life and the thermal energy

Problem

Model a rod-shaped bacterium as a cylinder of radius

r

and straight length

h

, capped at each end by a hemisphere of the same radius

r

(so the two hemispherical caps together make one full sphere of radius

r

). ((a)) Derive an expression for the total surface area

A

and total volume

V

of this shape in terms of

r

and

h

, and hence write down

A/V

. ((b)) A particular bacterium has radius

r = 0.5\,\mathrm{\mu m}

and total end-to-end length

2\,\mathrm{\mu m}

(so the straight cylindrical part has length

h = 2\,\mathrm{\mu m} - 2r

). Evaluate

A/V

for this cell, in

\mathrm{\mu m^{-1}}

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