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The shape of a bacterium can be approximated by a cylinder of radius r and height h capped on each end by a hemisphere. The volume and surface area of the bacterium are given by
It is known that the rate R at which a chemical is absorbed into the bacterium is R = c(S/V), where c is a constant of proportionality. Assume that for a certain bacterium, r = 0.9 ± 0.1 μm and h = 1.7 ± 0.1 μm.
- a. Are the computed values of S and V independent? Explain.
- b. Assuming the measurements of r and h to be independent, estimate R and find the uncertainty in the estimate. Your answer will be in terms of c.
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