More conceptual than numerical, (max/min problem)

N

NYC

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Oct 20, 2005
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Hey guys, its me again. Alright, my Calc professor likes these problems, and conveniently enough, I don't. Heh, any help on this would really be appreciated. (You guys are awesome) "A Right Circular Cone is to be circumscribed about a sphere of given radius. Find the ratio of the altitude to the base radius of the cone of least possible volume."
OK I've drawn up derivatives of volume equations, but I wind up with things like x=x....yeah...it's slightly aggravating. If you have any suggestions, that would be great.
 
We'll be glad to review what you've done, but you'll need to post it first.

Thank you.

Eliz.
 
Sorry!

Aye, sorry.
OK so I drew a diagram and found the area of the base radius of the cone and the area of the circle created with the sphere's diameter to be similar (I didn't want to provide my work because I wasn't sure how coherent it would be) I set the (area of circle in sphere)/(area of base of cone)=(altitude of cone)/(2*sphere's radius)

My problem is linking that ratio (which I'm not sure is right) to the equations for volume. V=1/3*(pi*r^2)(altitude) V'=2/3*h*pi*r+ 2/3*pi*(r^2) where r is that of the cone
So, yeah, I'm trying to see relationships in the problem, but thus far, it hasn't worked.
 
...

that's not nice...please, I could use some real help on this problem
 
I'm not sure how you're getting an "area" for the "radius of the base of the cone", since "radius" is a measure of length, not of area. Yes, the circle for the base and the circle for the cross-section of the sphere will be similar; all circles are similar, pretty much by definition. So I'm not sure how that helps at all.

You're needing to put a cone around a sphere. You might want to start by drawing the cross-sectional view, and try to relate the radius of the interior sphere to the height and/or radius of the exterior cone.

If you get stuck, please reply listing your steps. Thank you.

Eliz.

P.S. I have no idea who the loser is that posted the nonsense message above. If you contact the site admin, he may be able to remove this garbage from the thread.
 
Hi, NYC.

I've become quite interested in your question (and quite frustrated too).

I have my school Calculus exam on Wednesday, and lately I have been stealing people's questions and getting help to work through them. I realise this is quite evil, but in my defense I am thirsty for questions that I find difficult.

If you don't mind, I would like to post your question, giving reference, on http://www.sosmath.com/CBB/index.php, because there I can latex up my approach much more neatly than here and I'm relatively more accepted there, hence the chance of getting help greater.

Of course, I am perfectly fine with you desiring me not too.

I have found this
http://groups.google.com/group/alt.alge ... 8826c02191

Thanks,
Unco.

Edit: The post is here.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I do not intend this to hinder others from helping you. It's just a bit of "me me me" on my behalf.
 
A round of thanks

OK, Stapel, thank you very much for the assistance (VJ is my brother, he just made up a name so he could post one comment...kids these days, hah) Unco, feel free to use the problem however you want, and I'm grateful to you too. Galactus...wow....thank you so much......(did i mention that you guys are awesome?) Hah, until next time, peace guys
 
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