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Math Help - Vectors

  1. #1
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    Vectors


    (OSTP is the front of the cube incase you view it differently)


    A marble base for a statue is formed from a cube of side 7m. Is is placed relative to coordinates axes as shown in the diagram.
    A B and C divide ST UT and PT respectuvely, in ration 3 : 4.

    a) Find the coordinates of A, B, C
    I've done this part:
    A(3,0,7) B(7,4,7) C(7,0,3)


    b) If the corner of the cube is cut off along the plane defined by ABC find the surface area of the block.

    The initial surface area (hopefully) should be: 7 x7 x 6 = 294
    I tried finding the area of the 3 triangles (ACT) (ABT) (BTC) and subtract 294 by this but its wrong and don't know what to try next.

    Please help, thanks.

    Answer = 283.86m^2
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  2. #2
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    Hello, r_maths!

    You're that close to the correct answer . . .


    The surface area of the original cube is: .6 7 = 294 m.

    When that corner is sliced off, we lose three isosceles right triangles
    . . Each has 4m legs and an area of 8 m.

    Then we gain an equilateral triangle with side 4√2 m.
    . . Its area is: 8√3 m.


    The final surface area is: .294 - 3(8) + 8√3 . .283.86

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  3. #3
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    Thanks you.
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