#keplero’s area of a circle

1 messages · Page 1 of 1 (latest)

glacial grotto
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hi i was studying maths and i came across with keplero’s demonstration for the area of a circle (im sure some of yall are familiar with this). I was wondering if i could use the same principle for the volume of a sphere.

Like, divide a sphere in infinitesimally small pyramids that have an height = the radius, then the sum of their bases will be as much as the surface of the sphere (4pi*r^2).
I can “join” together all the pyramids to make a bigger pyramid with a surface of 4pir^2 and height = r.
Then the volume should be correct once i calculate the volume of the pyramid, right?

IMG_6052.jpg
fleet urchinBOT
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glacial grotto
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it’s because to find the volume of the sphere we used a theorem i don’t really like so i was looking for alternatives

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(we had used Cavalieri principle)

cyan salmon
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Yes, that works. Will just be an integral sum for a double integral instead of a single one.

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Though, do be careful with the limits.

glacial grotto
cyan salmon
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Ah. Well, then yeah.

glacial grotto
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Since i cant make calculations i guess i'll have to stick to cavalieri principle...

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But i hate remembering it haha

cyan salmon
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Though, do note that the bases of your pyramids need to not just decrease in area in the limit, but specifically in diameter.

glacial grotto
cyan salmon
# glacial grotto Wdym?

Diameter of a set is the maximum distance between its two points.
So, in the limit your pyramids can't have very thin, but at the same time very long bases.

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So, both dimensions of the base have to shrink.

glacial grotto
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well i cant make calculations yet so i dont really have to worry about it haha

cyan salmon
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Not sure how to make it nice to calculate, either.

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If I had to find the volume of the sphere, I'd just write an integral.

glacial grotto
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Its cause our teacher gave told us this thing that keplero did with no calculations, so i thought it was fine without them lmao

glacial grotto
agile spokeBOT
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@glacial grotto

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