Results 1 to 5 of 5

Math Help - A truncated pyramid.

  1. #1
    Newbie
    Joined
    Oct 2010
    Posts
    10

    A truncated pyramid.

    I have been trying to solve this one but i simply don't know how to. I asked my teacher about it and he said I should try to use the coefficient of similarity, but still no results. The task:

    The bases of a truncated pyramid have the surfaces (areas) of 98cm^2 and 2cm^2. Whats the surface (area) of a section that cuts trough the truncated pyramid and goes trough the center of the truncated pyramid's height and is parallel with the bases.


    Every help is welcome!
    Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    I have just one question. What is the shape of the base? Is is a square pyramid?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2010
    Posts
    10
    It isn't specified so it can be either one of them but i guess its a triangle in the base.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by IoNForce View Post
    I have been trying to solve this one but i simply don't know how to. I asked my teacher about it and he said I should try to use the coefficient of similarity, but still no results. The task:

    The bases of a truncated pyramid have the surfaces (areas) of 98cm^2 and 2cm^2. Whats the surface (area) of a section that cuts trough the truncated pyramid and goes trough the center of the truncated pyramid's height and is parallel with the bases.


    Every help is welcome!
    Thanks in advance.
    1. Draw a sketch (see attachment)

    2. Complete the frustrum to a pyramide as indicated in my sketch. The proportion of similar areas equals the proportion of the square of corresponding lengthes.

    3. Let t denote the top area (2 cm²), b the base area (98 cm²) and s the cross-section area.
    Then you know:

    \dfrac{y^2}{x^2} = \dfrac{98}2=49~\implies~y=7x

    4. The cross-section has the distance
    d = \dfrac{x+y}2
    from the top of the completed pyramide.
    Then you know:

    \dfrac{\left(\frac{x+y}2\right)^2}{x^2} = \dfrac{s}2

    Replace y by 7x:

    \dfrac{\left(\frac{x+7x}2\right)^2}{x^2} = \dfrac{s}2~\implies~\dfrac{(4x)^2}{x^2}=\dfrac s2~\implies~s=32
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2010
    Posts
    10
    Quote Originally Posted by earboth View Post
    1. Draw a sketch (see attachment)

    2. Complete the frustrum to a pyramide as indicated in my sketch. The proportion of similar areas equals the proportion of the square of corresponding lengthes.

    3. Let t denote the top area (2 cm²), b the base area (98 cm²) and s the cross-section area.
    Then you know:

    \dfrac{y^2}{x^2} = \dfrac{98}2=49~\implies~y=7x

    4. The cross-section has the distance
    d = \dfrac{x+y}2
    from the top of the completed pyramide.
    Then you know:

    \dfrac{\left(\frac{x+y}2\right)^2}{x^2} = \dfrac{s}2

    Replace y by 7x:

    \dfrac{\left(\frac{x+7x}2\right)^2}{x^2} = \dfrac{s}2~\implies~\dfrac{(4x)^2}{x^2}=\dfrac s2~\implies~s=32

    Thanks, I managed to do it with the new height (3x) and I forgot to reply here, sorry ><
    Anyway thanks a lot for the help!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. how many combinations if space is truncated
    Posted in the Statistics Forum
    Replies: 1
    Last Post: August 28th 2011, 03:18 PM
  2. Truncated Prism
    Posted in the Geometry Forum
    Replies: 1
    Last Post: February 27th 2010, 01:21 AM
  3. Truncated and Non-truncated distribution
    Posted in the Advanced Statistics Forum
    Replies: 7
    Last Post: July 27th 2009, 06:40 AM
  4. MLE of Truncated Bivariate Normal
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: October 8th 2008, 04:51 AM
  5. Truncated SVD
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: June 29th 2007, 09:07 AM

Search Tags


/mathhelpforum @mathhelpforum