Refer to Exercise 19. Assume that for a certain bacterium, r = 0.8 ± 0.1 μ m and h = 1.9 ± 0.1 μm.

a. Estimate S, and find the relative uncertainty in the estimate.

b. Estimate V, and find the relative uncertainty in the estimate.

c. Estimate R, and find the relative uncertainty in the estimate.

d. Does the relative uncertainty in R depend on c?

Step 1of 5:

The shape of a bacterium is approximated by a cylinder of radius r and h capped on each by a hemisphere. The volume and surface area of the bacterium is given by

V =

S = (h + 2r)

Where r = 0.8and h = 1.90.1. Here the rate R at which the chemical is absorbed to the bacterium is R = c (S/V), where c is a constant of proportionality.

We have to find

The estimate of S, and the relative uncertainty in the estimate. The estimate of V, and the relative uncertainty in the estimate. The estimate of R,and the relative uncertainty in the estimate. Whether the relative uncertainty of R depend on c.Step 2 of 5:

It is given that the surface area of the bacterium is S= (h + 2r)

The radius r =0.8 , and the uncertainty = 0.1 .

The height h = 1.9 ,and the uncertainty = 0.1 .

So the surface area of the bacteria

S =

=

= 17.584.

ln S = ln ( 2+ ln r + ln (h+2r)

In Order to find the uncertainty of the surface area we have to find the uncertainty of surface area due to each term.

Here

=

= 1.8214

And

=

= 0.2857

So the uncertainty in the estimate is

=

= 0.18 .

Therefore the estimate of the surface area of the bacteria is (17.58). And the uncertainty in the estimate is 0.18 .

So the relative uncertainty of the surface area

Relative uncertainty =

=

= 0.0102

Therefore the relative uncertainty of the surface area is 0.0102 .