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 2006-05-26, 07:19 #1 mfgoode Bronze Medalist     Jan 2004 Mumbai,India 22·33·19 Posts Cylinder, sphere and cone. Here is an easy one provided you remember the formulae. A cylinder whose height is the same as its diameter contains a sphere that exactly fits inside. A cone also exactly fits inside when the sphere is removed. What are the ratios of the respective volumes? Alpertron how about using Tex to demonstrate? Mally
 2006-05-26, 12:55 #2 alpertron     Aug 2002 Buenos Aires, Argentina 3×7×73 Posts The graph is: $\small\hspace{10}\unitlength{.75} \picture(250,250){~(125,225){\circle(200,40)}{~(125,25){\circle(200,40)}{~(25,30){\line(0,200)}{~(225,25){\line(0,200)}~(125,125){\circle(200,200)}{~(125,225){\line(-100,-200)}{~(125,225){\line(100,-200)}}$
 2006-05-26, 13:37 #3 Greenbank     Jul 2005 2×193 Posts Cylinder:Sphere:Cone = 3:2:1
 2006-05-26, 13:49 #4 alpertron     Aug 2002 Buenos Aires, Argentina 3×7×73 Posts Since h = 2r: Cylinder: pi*r^2*h = 2*pi*r^3 Sphere: (4/3)*pi*r^3 = (4/3)*pi*r^3 Cone: (1/3) r^2*h = (2/3)*pi*r^3 So what Greenbank wrote above is correct.
 2006-05-26, 17:20 #5 mfgoode Bronze Medalist     Jan 2004 Mumbai,India 22×33×19 Posts Excellent Greenbank and Alpertron for the sketch and answer. Note that the area of a spherical cap of depth h is equal to a a ring of the cylinder of the same width h. Mally
2006-05-28, 04:34   #6
mfgoode
Bronze Medalist

Jan 2004
Mumbai,India

80416 Posts
Spherical cap in section

Quote:
 Originally Posted by mfgoode Excellent Greenbank and Alpertron for the sketch and answer. Note that the area of a spherical cap of depth h is equal to a a ring of the cylinder of the same width h. Mally

Alpertron, I dont want to make a habit of this. Please can you display your dexterity with TEX and cut off from the top of your sketch about 2 cms. so only that portion remains (The top 2 cms), to be able to visualise what I mean viz: that the area of the spherical cap is equal to the ring of the cyclinder of the same depth. You may or may not ,as you wish remove, that part of the cone which remains which ever is easier for you.
Thank you,
Mally

2006-05-29, 20:04   #7
alpertron

Aug 2002
Buenos Aires, Argentina

3·7·73 Posts

Quote:
 Originally Posted by mfgoode Alpertron, I dont want to make a habit of this. Please can you display your dexterity with TEX and cut off from the top of your sketch about 2 cms. so only that portion remains (The top 2 cms), to be able to visualise what I mean viz: that the area of the spherical cap is equal to the ring of the cyclinder of the same depth. You may or may not ,as you wish remove, that part of the cone which remains which ever is easier for you. Thank you, Mally
From the documentation it appears that only entire circles can be drawn.

$\small\hspace{10}\unitlength{.75} \picture(250,150){~(125,25){\circle(200,20)}{~(125,125){\circle(200,20)}{~(125,75){\circle(200,20)}{~(125,75){\circle(175,15)}{~(125,125){\circle(200,200)}{~(25,25){\line(0,100)}{~(225,25){\line(0,100)}}$

 2006-05-30, 16:48 #8 alpertron     Aug 2002 Buenos Aires, Argentina 3·7·73 Posts I finally found the way to draw the sphere cap and cylinder!!! $\small\hspace{10}\unitlength{.75} \picture(400,150){~(200,25){\circle(350,30)}{~(200,125){\circle(350,30)}{~(200,125){\circle(320,19)}{~(200,200){\circle(350,350;204,336)}{~(25,25){\line(0,100)}{~(375,25){\line(0,100)}}$
 2006-05-31, 04:09 #9 mfgoode Bronze Medalist     Jan 2004 Mumbai,India 205210 Posts Cylinder and spherical cap. Excellent Alpertron and thank you very much. This is an improvement on your last sketch which also is very good. I will be sending you my photos for my avatar as soon as I can get my scanner to do the job. How do I send it on to you? By PM, e-mail or what? Mally P.S. Dont bother really, but if you could have shaded the cap by dotted lines as in a section I think the result would be more outstanding Last fiddled with by mfgoode on 2006-05-31 at 04:12

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