Results 1 to 2 of 2

Math Help - solid geometry sphere problem

  1. #1
    Newbie
    Joined
    Jul 2009
    Posts
    21

    solid geometry sphere problem

    A sphere having a radius of 6 cm rests on 3 horizontal wires forming a plane triangle whose sides are 5 cm, 12 cm and 13 cm. What is the height of the top of the sphere above the plane of the wires?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by fishlord40 View Post
    A sphere having a radius of 6 cm rests on 3 horizontal wires forming a plane triangle whose sides are 5 cm, 12 cm and 13 cm. What is the height of the top of the sphere above the plane of the wires?
    1. The tangent points of the sphere and the wires are placed on the incircle of the triangle. The incircle has the radius r. The sphere has the radius R.

    2. The triangle is a right triangle because 5^2+ 12^2 = 13^2

    3. Let A denote the area of the triangle. Then the radius of the incircle is calculated by:

    r = \dfrac {2A}{a+b+c} = \dfrac{ a \cdot b}{a+b+c}

    With your values you'll get r = \dfrac{60}{30}=2

    4. The height of the sphere above the triangle is h = R+h' with

    h'^2+r^2=R^2

    With your values you'll get: h'=\sqrt{32} = 4\sqrt{2}

    and consequently h = R+h'~\implies~h=6+4\sqrt{2}\approx 11.66
    Attached Thumbnails Attached Thumbnails solid geometry sphere problem-kugeldurchebene.png  
    Last edited by earboth; March 22nd 2010 at 12:07 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Solid Geometry
    Posted in the Geometry Forum
    Replies: 2
    Last Post: December 3rd 2011, 10:49 AM
  2. solid geometry problem
    Posted in the Geometry Forum
    Replies: 1
    Last Post: December 6th 2009, 07:49 AM
  3. Replies: 2
    Last Post: May 18th 2008, 04:45 AM
  4. Solid Geometry Help Needed
    Posted in the Geometry Forum
    Replies: 2
    Last Post: May 13th 2007, 03:48 PM
  5. Solid geometry help!!!
    Posted in the Geometry Forum
    Replies: 2
    Last Post: April 26th 2007, 08:34 AM

Search Tags


/mathhelpforum @mathhelpforum