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Components of $E .$ coli $E .$ coli cells are rod-shaped, about $2 \mu \mathrm{m}$ long and $0.8 \mu \mathrm{m}$ in diameter. The volume of a cylinder is $\pi r^{2} h$, where $h$ is the height of the cylinder. (a) If the average density of $E .$ coli (mostly water) is $1.1 \times 10^{3} \mathrm{g} / \mathrm{L},$ what is the mass of a single cell? (b) $E$. coli has a protective cell envelope $10 \mathrm{nm}$ thick. What percentage of the total volume of the bacterium does the cell envelope occupy? (c) $E$ coli is capable of growing and multiplying rapidly because it contains some 15,000 spherical ribosomes (diameter 18 $\mathrm{nm}$ ), which carry out protein synthesis. What percentage of the cell volume do the ribosomes occupy?

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Okay. So we need to prove that the surface area is six micrometers and the volume is one like meter cubic. And so it's cylindrical and lengthen the diameter. It was a long micro little radius. We are going to .5 microfilm readers. So there I have a cylinder is given by opposed to two pi R L being linked plus pi R squared plus pi R squared. We're just going to equal to two times three 0.14. Most amusing for by times 0.5 times two plus two times 3.1 four Times 45 sq. No, it's gonna give US seven. I didn't put units on that but it's micrometers squared times one volume equals pi R squared Times else. That's going to equal to 3.14 times 0.5 squared times two. My commuters cubic. We're just an equal to 1.5 Micro m. Cute. Which is equal to 1.5 my perimeters Cube Times two. Which are both close enough to verify that the area is equal to six micro leaders. The volume is equal to one micro with cubic Michael. Meet or not, peter sorry. So to find the fentaNYL Leaders of them, we know that 1000 liters is equal to one m cubic and Monsanto is equal 10 to 15 which means that right volume equals two one. My creator stupid. You're equals to one. My palm reader cubic times um Over 10 to the 6th micro meters and times 1000 the leaders over von reader. You do Times 10: 15. Whatever one leader equals to one the asset for the lot of bacteria and the weight of the cells. Democracy let's say they were the same boring decoys earlier. So we have we P. Equals 10 To the -18. He was cute. Total volume is 1028. So we have this equation B F. T. Equals and B. P Equals 10-28 Times 10 to the -18 meters cute equals turn to the turn meters cute. Which equals to 10 km cute the lesson that for the main space and you know the volume available. So We can assume that it's about 2/3 And from there take 2/3 of that. What will give us about Three times into the 14 m. Weird. So 10028 cells four or six times 10 to 16 years cubic equals 100 cells per millimeter cubic. Because the three I promise they will go.

So I'm running to the nearest thousands. The number I have ISS 16 0.99 fly and I need to find the thousands Place off. This is tense 100 thousands. My testing digit is a number next to it with five remembrance. It's five or greater. You're gonna round up. If it's war or less, it's going to stay. So in this case it is. Five were up, which is gonna make my roaming digit to go up. So right now I had 16 and 99 thousands. So if I'm gonna round it up instead of 99 is going to become 100 self since.

We need to use a calculator to find the value off. 10 for minus 2.9 point 23 rounded to four decimal places. First, let us input this value in the calculator. So it is then, uh, minus 2.95 to 3. Impressing. Enter. We get a little 0.111 Just being around. Answer to four decimal places. It is approximately 0.11