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Math Help - Maxima or minima?

  1. #1
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    Maxima or minima?

    Find the volume of the largest circular cone tat can be cut from a solid sphere of radius 4cm.


    My problem was not sure which equation can be use in this question....please help !

    Thx.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by sanikui View Post
    Find the volume of the largest circular cone tat can be cut from a solid sphere of radius 4cm.


    My problem was not sure which equation can be use in this question....please help !

    Thx.
    First thing to do is draw a labled diagram of a cone in the sphere.

    Now write the volume of the cone in terms of what you know and any free variables that you had to introduce when you labled the diagram.

    CB
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  3. #3
    Member u2_wa's Avatar
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    Quote Originally Posted by sanikui View Post
    Find the volume of the largest circular cone tat can be cut from a solid sphere of radius 4cm.


    My problem was not sure which equation can be use in this question....please help !

    Thx.

    I have attached a diagram to illustrate the answer.

    Let r be the radius of cone.
    height of cone= h=\sqrt{4^2-r^2}+4 (see diagram)
    r^2=4^2-(h-4)^2

    Volume of cone =\frac{1}{3}\pi.r^2.h<br />

    V=\frac{1}{3}\pi.(4^2-(h-4)^2).h

    calculate \frac{dV}{dh}=0<br />

    I got  h=\frac{16}{3}cm

    Put this value of h in equation V=\frac{1}{3}\pi.(4^2-(h-4)^2).h<br />
to get an answer.

    Hope this helps
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  4. #4
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    Answer is 79.43cm^3
    V^^
    Thanks.
    Last edited by sanikui; March 24th 2009 at 04:39 PM.
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