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Typically, large bacteria have the shape ofcylinders of fixed radius a and varia

ID: 1662900 • Letter: T

Question

Typically, large bacteria have the shape ofcylinders of fixed radius aand variable length L.

(a) Demonstrate that the surface-to-volume ratioof these bacteria does not depend on the length of thebacterium.

(b) Explain why a large cylindrical bacterium canfeed itself more efficiently than a large spherical bacterium.Assume that the bacteria feed by absorbing nutrients through theirsurface. Compare the surface areas of cylindrical and sphericalbacteria with the same volume for the same foodrequirement.

Explanation / Answer

Given Cyllindrical Bacteria radius = a length = L => Vol = a2L and S.A = 2aL S.A / Vol = 2/a => independent of "L" (b) If the vol of spehere and cylinder is same => (4/3)a3 = a2L => 4a = 3L => L = 4a / 3 Bacteria with more surface area will feed efficeintly SA of sphere , S= 4a2 SA of cylinder , S' = 2aL S' / S = L/2a = (4a/3) / 2a