In general, large bacteria have the shape of a cylinder of a radius r and a...

In general, large bacteria have the shape of a cylinder of a radius r and a very long length h, where h >> r. This is due to the fact that a large cylindrical bacterium can feed itself more efficiently than a large spherical bacterium. To check whether this is true or not, assume there are two bacteria, one cylindrical (with h >> r) and one spherical with radius R where they have the same volume, and thus the same food requirements. Furthermore, assume that the bacteria feed by absorbing nutrients through their surfaces. (a) First, show that the surface-to-volume ratio of these bacteria does not depend on the length of the bacterium. (b) Calculate the surface-to-volume ratio of a sphere of radius R. (c) Make an argument why a large cylindrical bacterium can feed itself more efficiently than a large spherical bacterium. (You should able to argue that the radius of the cylindrical bacteria is smaller than the radius of the spherical bacteria, i.e. r << R).

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