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A typical human cell is approximately 11.0O um in diameter and enclosed by membrane that is 6.000 nm thick: What is the volume of the cell including the membrane? T...

Question

A typical human cell is approximately 11.0O um in diameter and enclosed by membrane that is 6.000 nm thick: What is the volume of the cell including the membrane? To simplify the calculations, model the cell as sphere_total volume:992 x1OIncorrectWhat is the volume of the cell membrane?-12 2.3 xlOmembrane volume:IncorrectWhat percent of the total volume does its membrane occupy?membrane percentage: 0.329um}uni

A typical human cell is approximately 11.0O um in diameter and enclosed by membrane that is 6.000 nm thick: What is the volume of the cell including the membrane? To simplify the calculations, model the cell as sphere_ total volume: 992 x1O Incorrect What is the volume of the cell membrane? -12 2.3 xlO membrane volume: Incorrect What percent of the total volume does its membrane occupy? membrane percentage: 0.329 um} uni



Answers

Biology A typical human cell is approximately $10 \mu \mathrm{m}$ in diameter and enclosed by a membrane that is $5.0 \mathrm{~nm}$ thick. (a) What is the volume of the cell? (b) What is the volume of the cell membrane? (c) What percentage of the cell volume does its membrane occupy? Model the cell as a sphere.

All right. This problem gives us two different types of cells and wants to know which one is going to be more efficient based on the volume in the service area. And so first, let's look at the numbers they give us. They tossed the liver cell has a volume of 5000 micro meters. Cute. I'm not gonna write the units is to save space and keep it a little more simple. And it tells us the service area is 100 and 10,000 micro meters squared on, and then on the other side, we have a pancreatic cell that has a volume on your celebrities of 1000 micro meters Q in a surface area of 13,000 micro meters squared. And so we need to figure out what is the ratio of of all you to surface area and whichever one has a greater ratio is gonna be the one with the most surface area per volume and therefore is gonna be more efficient. And so the simplest way to figure this out is the simply divide. So if we go over here and we divide 110,000 by 5000 we would get 22 and then if we go over here, we would divide 13,000 by 1000 and we would get 13. And so what these two answers tell us is that the ratio of surface area to volume for the liver cell is 22 in the ratio of surface area to volume for the pancreatic cells 13. And so because the liver cell number is larger, that means that there is less volume taken up per surface area and therefore it has more surface area and is going to be more.

In this problem, we're going to calculate the thickness off that. Remember, that is what we call D in order to kill clergy sickness. Let's write the formula for the capacitance and Sequels Toe cup up. After all, not everyone by D when this couple that elected constant that's not not is the permit Ugo respects as the area off the charge plates. Now we can write this question as a city wanted by equals. Two. Cover That's run Not you wanted by D. Now it's only been squared for TV can White. It has a equals toe cop that's no, not be worried by C. R. A. What deceives the contestants or the best of their school iniquity. Number one Nobody in sending Weathers into disquieting weaken White D equals two. I'll be of the couple years as a three point digital and then 8.85 Multiply Way turns bar minus 12. Well, im squared for Newton Meters Square you wanted by the contestants, but unit area is one. Multiply. Britain is far minus six foot out. You wanted by Duris Barra minus four meters square, so this would be divided for Dia de equals two 26.55 Multiply return It's far minus 10 Mito. It can be written as a D equals toe 2.7, Madam, you do So this is the required answer. Thank you.

In this problem of Into the center of physics we have given that although human cells vary in size, the volume of a typical cell is equivalent to the volume of a sphere. That approximately 10 to the power five m radio. So this is a this is the typical radius of uh cell is almost 10 to the power minus five me to say this is a typical cell. And now we have to estimate the number of cells in your body. So let's suppose we are starting from the weight of your body. So your body weight is in cages. This would be around 75 kg. And now when we want to find the volume of her body so this value would be say volume of your body save Phoebe would be around 75 kg. And we have the conversion factor that it's one kg of equal. So 10 to the power minus three meter cube volume. So this value would weigh 75 multiplied by 10 to the power minus three and meter cube. So this is the volume of your body. And now this is the volume of a typical salad around. Say this in despair and volume of the sphere is around This is food divide with three and by and this is the radius of the cells said this is R. c. and Cube. Now this really would be full divide with three and pie. That is 22 divided with seven and radius of a cell is approximately 10 to the power -5 m. So this where they would be 10 to the power -5 and cubic times of this. So that's where we'll be cubes. And since these emitters of media will be all cute since this is the volume of ourselves say we s. Is here. So we say we say that is the volume of the self and this is the volume of the body. So from here we say that the volume of the body and we know that body is composed of self. So that means the volume, the volume of the total number of cells would be equal to the volume of the body. So we will apply the concept say we don't have the numbers so we have to multiply the numbers and this value is multiplied with volume of a single cell. From here we have to calculate the value of end. So value of energy equal to we be divided with obviously which is equals two. Now put the value 75 multiplied with 10 to the power minus three. This is meter cube and divided with We have to multiply it so there should be four multiply with 22. That is equals to 88 Divided with three. Multiple 700 equals to 21 multiply with this is multiplied with minus five, multiplied by three. So this valuable with minus 15 and value is meeting you. So meter cubed two m cube is canceled out and we have to proceed further. So N is equal to 75. Now this has to be multiplied with 75. So 75 multiplied with 21 divided with 88. And this is power is again some power has been canceled out and This is where they will return to the power -3 plus 15. No, 75 It's multiplied with 21/8 equals to 1575 is divided with 88 Is equal still 17.89 or weekends at age 18. And multiply with 10 to the power, there's a minus three plus 15 equals to 12. So when we saw that this is equal to 1.8. Multiplied by 10 to the power. This is Power is one added because we have moved our decimal place to the left hand side. So this way we would be 13 cells. That means We can say your body contains 1.8, multiplied by 10 to the power 13 cells.

Converting from cubic micro meters two cubic millimeters. It's easiest to go through cubic meters in the middle. We know that for every one meter there are tend to the sixth Micro meters. But since we're working with cubic make readers, we have to cube this denominator in. Since we cubes the denominator, we also have a cube. The numerator. Yeah, this is no equal to one cubed meters cute and one cubed is just one. So one meter cute. The bottom is equal to 10 to the sixth cubed Michael meters cute and 10 to the sixth. Cubed is also equal to 10 to the 18th converting. Then we know there are 1000 or 10 to the third millimeters in one meter. But since we have meters cubed here, I need to have meters cubed here as well. So we could you be the denominator. But since we cube the denominator again, we have to queue the numerator. It's no. We have 10 cubed cube, more 10 to 9 millimeters cute and one cube or one meters cute. So our cubic Mecham eateries will cancel and our cubic meters canceled and we'll be left with cubic millimeters converting doing this is equal to 2.56 times. Tend to the negative night millimeters cute converting Next. We want to know the volume of tend to the fifth cells in leaders converting What we can do here is convert the volume of one cell into leaders and the multiply that value by 10 to the fifth. An important relationship to know here is that one Dustin meter cubed is equal to one leader, so we can convert our 2.56 Migra meters cubed to decimate is cute and that will be the same as the volume in leaders. So we start with 2.56 Micra meters Q. And we multiply by one meter over 10 to the sixth micro meters. Then we have to cube both of these because we're working with micro meters, cute and free raised the denominator to the third power. We also have to raise the numerator of her power converting Austin for every one meter. Here are 10 dosimeters and again we have to queue both of these. Since we're working with meters cubed here, this year's then one meter cute since one cute is still one, then we have tend to the A team Micro meters cute since 10 to the sixth to the third power is 10 to the 18th. Then we have tend to the third estimators cute and one meter cute. Our cubic macro meters cancel and our cubic meters cancel and we're left with just metres cubed or leaders converting For doing the math we get 2.56 times 10 to the negative, 15 just meters cute or 2.56 times 10 to the negative 15th leaders. This is the volume for one cell and since we want the volume bird 10 to the fifth cells, we can dress Multiply this by 10 to the fifth and we get a total volume of 2.56 times 10 to the negative temp leaders.


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