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Math Help - 1 sphere on top of 4 spheres

  1. #1
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    1 sphere on top of 4 spheres

    hi, I have this question.
    4 spheres of radius 10 are placed on a table so that each touches 2 others. another sphere is placed on top. Find the height of the top of this fifth sphere above the table.
    thanks
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  2. #2
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  3. #3
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    Quote Originally Posted by Wilmer View Post
    hi, i've read it through but I dont know how this would help. thanks
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  4. #4
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    Hello, xiukhung!

    Four spheres of radius 10 are placed on a table so that each touches 2 others.
    Another sphere is placed on top.
    Find the height of the top of this fifth sphere above the table.

    The centers of the four spheres form a square with side 2r.
    It is r units above the table.

    The center of the fifth sphere forms a square-base pyramid.
    All of its edges have length 2r.

    We find that the height of this pyramid is \sqrt{2}\,r.

    The top of the fifth sphere is r units above the pyramid.


    Hence, the top of that sphere is: . r + \sqrt{2}\,r + r \:=\:\left(2 + \sqrt{2}\right)r units high.

    Answer: . 10\left(2+\sqrt{2}\right)\text{ units.}

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  5. #5
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    Thanks a lot, what about this problem?
    A sphere of radius length 8cm rests on top of a hollow inverted cone of height 15 cm whose vertical angle is 60 degrees. Find the height of the centre of the sphere above the vertex of the cone.
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  6. #6
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    Quote Originally Posted by xiukhung View Post
    Thanks a lot, what about this problem?
    A sphere of radius length 8cm rests on top of a hollow inverted cone of height 15 cm whose vertical angle is 60 degrees. Find the height of the centre of the sphere above the vertex of the cone.
    I'm not certain if I understand your question correctly.

    If the attached image describes the situation completely then you'll get x by using the Sine function:

    \sin(30^\circ) = \frac12 = \frac8x

    Solve for x.

    By the way: If you have a new question use a new thread. Otherwise you risk that no member of the forum will realize that you need further assistance.
    Attached Thumbnails Attached Thumbnails 1 sphere on top of 4 spheres-kugelinkegel2.png  
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