Solution Found!
The shape of a bacterium can be approximated by a cylinder
Chapter 3, Problem 19E(choose chapter or problem)
The shape of a bacterium can be approximated by a cylinder of radius and height
capped on each end by a hemisphere. The volume and surface area of the bacterium are given by
\(V=\pi r^{2}(h+4 r / 3)\)
\(S=2 \pi r(h+2 r)\)
It is known that the rate 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, \(r=0.9 \pm 0.1\ \mu m\) and \(h=1.7 \pm 0.1\ \mu m\).
a. Are the computed values of and
independent? Explain.
b. Assuming the measurements of and
to be independent, estimate
and find the uncertainty in the estimate. Your answer will be in terms of
.
Equation Transcription:
Text Transcription:
V={pi}r^2(h+4r/3)
S=2{pi}r(h+2r)
R=c(S/V)
r=0.9{+/-}0.1 m
h=1.7{+/-}0.1 m
Questions & Answers
QUESTION:
The shape of a bacterium can be approximated by a cylinder of radius and height
capped on each end by a hemisphere. The volume and surface area of the bacterium are given by
\(V=\pi r^{2}(h+4 r / 3)\)
\(S=2 \pi r(h+2 r)\)
It is known that the rate 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, \(r=0.9 \pm 0.1\ \mu m\) and \(h=1.7 \pm 0.1\ \mu m\).
a. Are the computed values of and
independent? Explain.
b. Assuming the measurements of and
to be independent, estimate
and find the uncertainty in the estimate. Your answer will be in terms of
.
Equation Transcription:
Text Transcription:
V={pi}r^2(h+4r/3)
S=2{pi}r(h+2r)
R=c(S/V)
r=0.9{+/-}0.1 m
h=1.7{+/-}0.1 m
ANSWER:
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