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Math Help - Cylinder and Cone

  1. #1
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    Cylinder and Cone

    There is a Cylinder with maximum volume into a Cone.
    The diameter of the Cone is 10 cm and the generator of the Cone is 13 cm.
    How much is the area of Cylinder ?
    I can't find any relationships between the Cone and Cylinder.

    The answer is 440*pi/3 cm^2
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  2. #2
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    Greetings:

    For simplicity, the cone and cylinder are shown using a single side view - the cylinder shown in dark red. Choosing the cone's vertex as origin, and given cone diameter and lateral edge length at 10 and 13 respectively, the altitude is deduced via Pythagoras at 12, and the diagram is thus explained. The volume of a right cylinder comes by product of its base area and height. If you use the values diagramed below, the volume is easily expressed as a function of radius, "r sub-c". Finally, differentiate the volume function, V, and set resulting derivitive equal to zero, i.e., let V' = 0 (why?). Solve V' = 0 for r sub-c and you'll have the radius of the cylinder whose volume exceedes all others. I shall assume you capable of determining the corresponding height and alas the cylinder's surface area. (circular "top and bottom" as well as lateral periphery).

    Regards,

    Rich B.
    Attached Thumbnails Attached Thumbnails Cylinder and Cone-clr.jpg  
    Last edited by Rich B.; December 24th 2005 at 04:13 PM.
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  3. #3
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    I am not able to find the diagram.

    This link doesn't work: [img]aolemb://792ED401-7379-11DA-9F02-0010B5094180/Untitled.jpg[/img]
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  4. #4
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    Hi:

    Yes, I see...scratching head while proclaiming aloud "now I know there was a diagram when I submitted yesterday"...
    I am sorry, I don't know where it went or why it even loaded as an address rather than the diagram that I'm sure I pasted into the very same field as the text. I will do my best to get a diagram off to you the moment time permits...Santastuff you know.

    Regards,

    Rich B.
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  5. #5
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    diagram has arrived

    Totalnewbie:

    See my original response to your query for the diagram promised earlier today. I hope this helps.

    Regards,

    Rich B.
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  6. #6
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    Any comments ?
    V = volume of cylinder
    I have to take the first derivative of radius.
    If I do it and and set derivative equal to zero then r = 10/3 and respectively height of cylinder = 4. What's wrong ?
    Attached Thumbnails Attached Thumbnails Cylinder and Cone-cylinder.jpg  
    Last edited by totalnewbie; December 26th 2005 at 05:59 AM.
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  7. #7
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    I suppose the answer 440*pi/3 cm^2 which is on the book, must be wrong.
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  8. #8
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    Quote Originally Posted by totalnewbie
    I suppose the answer 440*pi/3 cm^2 which is on the book, must be wrong.
    Hello,

    all results are correct: You get the greatest volume of the cylinder if r=10/3.

    In the problem is asked for the area of this cylinder. If you plug in the radius and the corresponding height you'll get the value given in the book.

    Greetings

    EB
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