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.

V = ar (h + 4r/3) S = 2nr(h + 2r)