2007-08-17 08:41:52 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
I'm talking about the distance from one corner to an opposite corner.
2007-08-17 08:47:38 · update #1
I'm guessing you didn't quite word this correctly since one other person responded with the length of one edge is it's maximum width ... but if you turn a cube on it's corner (like a top), you can spin it, and this cube will have a 'diagonal' between two opposite corners that is much longer than each edge. With this in mind, let's use a little algebra to figure this one out.
Remember Pythagorus ... the ancient greek mathematician who was counting square tiles while taking a bath? Here's his equation for right triangles:
a^2 + b^2 = c^2
Well, we're going to need to use this twice, because we're going to deal with not only a regular cube edge to calculate this, but also the diagonal along a flat surface will be used to calculate the diagonal between opposite corners.
Let 'e' = the length of an edge on the outside of the cube
Let 'd' = the length of a diagonal across one of the faces of a cube
Let 'x' = the length of the longest diagonal between two opposite corners of a cube which passes directly thru the center
finding 'd' is easy ...
d = sqrt ( e^2 + e^2 )
d = sqrt (2) * e
finding 'x' is almost as easy
x = sqrt ( e^2 + d^2 )
x = sqrt ( e^2 + 2e^2 )
x = sqrt ( 3e^2)
x = sqrt (3) * e
so ... to answer your question ... yes ... the maximum width of a cube is (in fact) the square root of 3 times the length of one of the edges.
2007-08-17 08:54:10 · answer #1 · answered by Daniel R 2 · 1⤊ 0⤋
What? If you know the length of the edge, you know the width. It's a cube...
[Edit]
Oh oh, yeah. For a 2D square, its
root(2*a^2)
For a cube, bottom corner to opposite top is:
root(3*a^2)
So its the square root of 3 times the *square* of the side.
[Edit 2]
Oh, your wording was confusing. Yeah it's root(3)*a , the way I read it I thought you meant root(3a).
2007-08-17 08:45:32 · answer #2 · answered by Jon G 4 · 3⤊ 1⤋
Yes, but it's better to say "the maximum length of diagonals of a cube".
2007-08-17 08:48:02 · answer #3 · answered by sahsjing 7 · 1⤊ 0⤋
Yes, sqrt(3).
If the cube does not have equal sides, then it's:
Diagonal = sqrt( a^2 + b^2 + c^2)
Where a, b, and c are the length of the sides.
2007-08-17 08:50:03 · answer #4 · answered by morningfoxnorth 6 · 0⤊ 1⤋
Did you mean the maximum length of a diagonal?
If so, yes!
2007-08-17 08:48:51 · answer #5 · answered by Amit Y 5 · 1⤊ 0⤋
It is actually called the "spatial diagonal".
2007-08-17 08:49:57 · answer #6 · answered by Larry C 3 · 1⤊ 0⤋