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 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.

Answer:

Step 1 of 4:

Given the shape of a bacterium can be approximated by a cylinder of radius r and height h capped on each end by a hemisphere.

Given the volume and surface area of the bacterium are

The rate R= c(S/V)

Given that for a certain bacterium, and