Typically large bacteria have the shape of a cylinder of fixed radius a and variable length L where L >> a. (a) Show that the surfacetovolume ratio of these bacteria does not depend on the length of the bacterium (dont bother adding on the areas of the end caps).

Typically large bacteria have the shape of a cylinder of fixed radius a and variable length L where L >> a. (a) Show that the surfacetovolume ratio of these bacteria does not depend on the length of the bacterium (dont bother adding on the areas of the end caps).

Contrast this with the surfacetovolume ratio of a sphere of radius R. (b) Explain why a large cylindrical bacterium can feed itself more efficiently than a large spherical bacterium. Assume that the bacteria feed by absorbing nutrients through their surface. To do this compare the surface areas of cylindrical and spherical bacteria that have the same volume and thus for the same food requirements. (You should assume that the radius of the cylindrical bacteria is smaller than the radius of the spherical bacteria i.e. a << R).

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