20060526, 07:19  #1 
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·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 
20060526, 12:55  #2 
Aug 2002
Buenos Aires, Argentina
3×7×73 Posts 
The graph is:

20060526, 13:37  #3 
Jul 2005
2×193 Posts 
Cylinder:Sphere:Cone = 3:2:1

20060526, 13:49  #4 
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. 
20060526, 17:20  #5 
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}×3^{3}×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 
20060528, 04:34  #6  
Bronze Medalist
Jan 2004
Mumbai,India
804_{16} Posts 
Spherical cap in section
Quote:
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 

20060529, 20:04  #7  
Aug 2002
Buenos Aires, Argentina
3·7·73 Posts 
Quote:
What about this? 

20060530, 16:48  #8 
Aug 2002
Buenos Aires, Argentina
3·7·73 Posts 
I finally found the way to draw the sphere cap and cylinder!!!

20060531, 04:09  #9 
Bronze Medalist
Jan 2004
Mumbai,India
2052_{10} 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, email 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 20060531 at 04:12 
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