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Express the edge length of a cube as a function of the cubes diagonal

  1. Jan 24, 2006 #1
    Hello,
    Here is my what am trying to solve.
    Express the edge length of a cube as a function of the cubes diagonal. Then express the area as a function of diagonal length if the side is x.

    This is what i know. The area of a cube is 6x^2 where x is the length. But in the problem i have to express the side length as a function of cubes diagonal. Can someone suggest me the relation between the side length and the diagonal, thanks.
     
    Last edited by a moderator: Jan 7, 2014
  2. jcsd
  3. Jan 24, 2006 #2
    Think abut the pythagorean theorem and what is true about cubes but not about all rectangular prisms.

    And I'm not entirely sure from your post whether you want a formula for surface area or volume.
     
  4. Jan 25, 2006 #3
    Okay on using the pythagorean theorem am getting
    y=2x^2 where y is the diagonal lenght and x is the side length.

    Now the area of the cube = 12x^4
    am i right. Plz let me know
     
  5. Jan 25, 2006 #4

    StatusX

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    You gave the corret area formula in your first post. And remember that the pythagorean theorem is a2+b2=c2. You forgot to square c in your formula. And are you interested in the diagonal of a face or of the whole cube? Because they have different lengths.
     
  6. Jan 26, 2006 #5
    Thanks for correcting me. Now i have y=sqrt 2x

    the area of the cube will be 24 x2
    The question says "express the area as a function of diagonal length", so am not sure whether to consider the diagonal of a face or the whole cube. 24x2 will be the answer right.
     
  7. Jan 26, 2006 #6

    HallsofIvy

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    Be careful- the "diagonal" of a cube is NOT the diagonal across a face. It is the line from one vertex of the cube to the opposite vertex. Yes, if y is the length of a side, then [itex]x= \sqrt{2}y[/itex] is the length of the diagonal of a face of the cube. Now, the diagonal from one vertex of a cube to its opposite vertex is the hypotenuse of a right triangle, having one side of length y and the other [itex]\sqrt{2}y[/itex]. If you let z be the length of that diagonal, z2= y2+ 2y2.
     
  8. Jan 26, 2006 #7
    Thanks, so the length of the diagonal will be z2=3y2
    Then the area will be 18y2 square units. Please correct me if am wrong, thank you.
     
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