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Math Help - radius and height of cone

  1. #1
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    radius and height of cone

    Hi I have done these types of problems but I have missed something this time.

    Have a circle with radius of 10. I remove a sector with an angle at the radius of 120 degrees. the remains of the circle (looks like pac-man) are joined to make perfect cone (no overlapping).

    I need to find the radius of the base of the cone and the vertical height of the cone from the centre to the point.

    My thoughts are:

    1.calculate the circumference of the circle remains ie. (360-120)*2*pi*10=40pi/3
    2. find r for base of cone. 40pi/3=2pi(r)-->40pi/3/2pi=r.
    3. side view of cone will be 2 congruent right triangles sharing vertical side with hyp =10.
    4. Use pythag to solve for height h^2=10^2-(40pi/3/2pi)^2.


    Any thing wrong with my method?

    Thanks,
    Neverquit
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  2. #2
    MHF Contributor
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    Seems correct to me.
    1.calculate the circumference of the circle remains ie. (360-120)*2*pi*10=40pi/3
    This should be (360-120)/360*2*pi*10, but 40pi/3 is correct.
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