Optimization II - Cylinder in a Cone

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[AP-sezs]

Thank you very much sir. The x-y plane concept was very helpful!!

[fiatiyaoconfidence]

very practical to understand.we want more of such videos

[fledbeast]

How do you know to subtract 2r from 8 to get the height? I understand that since the cylinder is less than the height of the cone it'd be subtracted from 8, but why 2r? Also why do you do 8 divided by 4-r and not 8 divided by r?

[iversonpaulalay]

So uhm... I dunno if this is gonna be seen, given that it's a 5 year old video, but first of all, thank you for the lesson! And secondly, should the height and radius of the cylinder always be the same or it's only for this case? Thank you!!!

[hammyhammoon]

Sir hello
Uhmm what if theres a question
Express the height h of the cylinder as a function of r?
Hope.u notice sir😅

[GururajMohan]

Can you please clarify how you wrote linear equation h=8-2r in a jiffy :-) Curious to know the details behind the equation. Yes, understood the similar triangles part. Thank you.

[JH-qnng]

Thank you sir, you've cleared my doubt!

[bhaskardas]

Do we get the minimum volume when r=0?

[joselynpacificar]

This was the easiest way ive ever seen in all the videos that ive watched. Thanks a lot

[jonathanandersen]

How did you make that animation in Geogebra?

[Gnerf]

A cone is MAYBE half the volume of a cylinder



1/2(b1 + 0) x height

base2 is 0 because the tip of the cone has an area of 0 or an area that is infinitely small. This may prove that a cone is half the volume of a cylinder. Let me know what you think!