Results 1 to 3 of 3

Math Help - cutting cuboids!!

  1. #1
    shosho
    Guest

    cutting cuboids!!

    A sculptor works with large wooden cuboids (rectangular prisms), cuts them into three smaller cuboids and then paints them black, white and grey. The volume of the black cuboid is always twice the volume of the white one and the volume of the white cuboid is always twice the volume of the grey one.

    The attached diagram shows how this works. The cuts are always parallel to the face marked with w and h. We will always denote the surface areas of the separated cuboids by A1(black ) A2 (white) A3 (grey)


    a)the sculptor is given a block for which l=1, w=6, h=3 Show that with these values the ratio of A1 to A2 is 3:2

    b) show that for any cuboid the sculptor cuts A1 is always less than 2(A2)

    c)the sculptor wants a cuboid with h=w which will give A1=3(A3). what would be the value of l in terms of w

    d) the sclptor decides she would like to have A1:A3 = 4:3. If this is to be the case find a formula linking l,w,h and give an example of the dimension of a cuboid before it is cut for which this will work.


    please help me!!! im in strife!! this q is absolutley impossible
    Attached Thumbnails Attached Thumbnails cutting cuboids!!-box.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    May 2007
    Posts
    3
    send to me at <Email address removed>
    Last edited by CaptainBlack; May 26th 2007 at 11:58 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by shosho View Post
    A sculptor works with large wooden cuboids (rectangular prisms), cuts them into three smaller cuboids and then paints them black, white and grey. The volume of the black cuboid is always twice the volume of the white one and the volume of the white cuboid is always twice the volume of the grey one.

    The attached diagram shows how this works. The cuts are always parallel to the face marked with w and h. We will always denote the surface areas of the separated cuboids by A1(black ) A2 (white) A3 (grey)


    a)the sculptor is given a block for which l=1, w=6, h=3 Show that with these values the ratio of A1 to A2 is 3:2

    b) show that for any cuboid the sculptor cuts A1 is always less than 2(A2)

    c)the sculptor wants a cuboid with h=w which will give A1=3(A3). what would be the value of l in terms of w

    d) the sclptor decides she would like to have A1:A3 = 4:3. If this is to be the case find a formula linking l,w,h and give an example of the dimension of a cuboid before it is cut for which this will work.


    please help me!!! im in strife!! this q is absolutley impossible
    The surface area of a cuboid with dimensions W, D, H is:

    A(W,D,H) = 2W*D + 2W*H + 2D*H

    That is there are six faces two of dimensions W,D, 2 of dimensions W,H
    and 2 of dimensions D, H.

    Now the surface areas of the three cuboids are:

    A3 = 2w*l + 2w*h + 2l*h

    A2 = 2w*(2*l) + 2w*h + 2(2*l)*h

    A1 = 2w*(4*l) + 2w*h + 2(4*l)*h

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Cutting stick
    Posted in the Statistics Forum
    Replies: 1
    Last Post: May 3rd 2011, 09:47 AM
  2. Cutting a quadrilateral
    Posted in the Geometry Forum
    Replies: 2
    Last Post: November 24th 2010, 08:20 AM
  3. cutting the cube
    Posted in the Math Puzzles Forum
    Replies: 5
    Last Post: October 15th 2010, 11:41 PM
  4. a maximum problem with cuboids!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 21st 2009, 05:37 AM
  5. cuboids
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 6th 2008, 08:30 AM

/mathhelpforum @mathhelpforum