SOLUTION: A diagonal of a cube joins 2 vertices not in the same face. If the diagonals are 4root3 cm long, what is the volume?

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Sketch the cube. Sketch in the 4sqrt3 diagonal
Let "x" be all the sides of the cube.
The diagonal of the base is xsqrt2
The 4sqrt3 diagonal is the hypotenuse of a triangle whose other
sides are "x" and 4sqrt3.
Then x^2+(xsqrt2)^2 = (4sqrt3)^2
x^2+2x^2 = 16(3)
3x^2=16(3)
x^2=16
x=4 (the side of the cube)
Volume = side^3 = 64 cu cm
Cheers,
Stan H.