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If each cube side is of length s, then the diagonal of the BASE is from Pythagorean theorem
sqrt ( s^2 + s^2) = sqrt (2) times s = 1.414s
The height of the cube is s, so we use the theorem again using the base diagonal and height to get the cube diagonal:
sqrt( (1.414s)^2 + s^2) = sqrt (3s^2) = sqrt(3) times s = 1.732s
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Continue Learning about Geometry
What is the name of the longest diagonal of the cube?
The principal diagonal.
Whats the edge length of a cube with a diagonal of 9ft?
The edge length of a cube with a diagonal of 9 ft is: 5.196 feet.
What is the shape of the cross section of a cube if the cut is made across the diagonal of the cube?
Rectangle
How do you use a Pythagorean theorem with cube?
You can use pythagorean theorem twice to find the diagonal of a cube
If the volume of a cube is 125 find the length of one of the face diagonals of the cube?
find the cube root of 125(which is 5) is the length of one side do Pythagorean theorem to find the diagonal 5squared plus 5 squared=50 square root of 50=7.07106781 is diagonal
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