WEBVTT
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Alright, so I've taken the liberty of doing two
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things here, I've written down all of the values
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that we have for the cross sectional areas. We're
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here on the left side. And I have also
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written out there mid points here in the second column
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. Um and remember that to find the midpoint,
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we just add we just take the average of these
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two values. zero was 18 over to equals nine
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and 18 58/2 years, 30 years and we did
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that for all of these. Um it's rather time
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consuming, but this is going to be the result
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. Um After that, what midpoint rule tells us
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Is that in order to approximately the volume here we're
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going to need to uh take 1.5 which is the
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distance between the cross sections. And we multiply 1.5
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x nine, Which is one minute point, then
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add to that 1.5 times 30 years. Then add
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to that 1.5 times 68.5 et cetera. And we
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can also uh do something somewhat simpler, which is
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first we add all of these midpoint values and then
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we multiply by 1.5 we just distribute us uh The
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1.5. So um uh if you add up all
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these mid points you can do this by hand.
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I wouldn't recommend it, I just do a calculator
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but if you add all these up you are going
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to get 900 Which is pretty useful because that means
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that multiplying by 1.5 is very easy. 1.5 times
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900 is just going to be 1350. So we're
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going to get uh, 1350. Now, of
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course, we need units for this. Can't just
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save 13.50. So we recall the units that we
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had, um, the areas were measured in square
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centimeters and then 1.5 was the distance between the cross
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sections in centimeters. So our units are just going
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to be cubic centimeters because we have spare centimeters multiplied
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by regular centimeters. So we have 13 50.
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Keep accelerators. That is going to be our approximation
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for the volume. Hey,