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Assuming the alveoli are spherical, what is the diameter of a typical alveolus?A. 0.20 $\mathrm{mm}$B. 2 $\mathrm{mm}$C. 20 $\mathrm{mm}$D. 200 $\mathrm{mm}$
0.2 $\mathrm{mm}$
Physics 101 Mechanics
Chapter 1
Models, Measurements, and Vectors
Physics Basics
Simon Fraser University
Hope College
McMaster University
Lectures
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This is Chapter one problem 68. So in this problem, we're looking for the diameter of a typical Al Viola ce. And we're told the alveoli are I are spherical where we're told to assume that and we're given the volume of one Alvey Elice so knowing the volume of a sphere is as written here, volume is 4/3 pi r cubed. Since we know the volume of a typical Al Viola s, we can rearrange that equation to use the volume to solve for the radius and then we'll just double the radius to get the diameter. So re arranging that top equation we have three V three times. The volume over for pie is equal to are cute So the pew root of that is going to be a radius and so we're going to take the volume were given in micro meters cubed. Plug it in there and we can solve to find that the radius is about roughly one 100. Make it meters and so that means that our diameter, which we're looking for, is about 200 micro meters. But if we look at our answer choices, these are all in millimetres. We've gotta convert from micro meters two millimeters. Yeah, and we can do that by noticing Micro is 10 to the minus six. So they're going to be 10 to the sixth Micro meters in a meter. And Mila is 10 to the minus threes. They're going to be 10 to the third millimeters also in a meter. So essentially, we're taking this number 202 100 micro meters and dividing by 10 to the third or dividing by 1,000 to get oh, point two 0.20 millimetres as our final answer. So the answer is a pretty small.
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