If the greatest distance between any two points on a cube is 8 inches, what is the volume of the cube, in cubic inches? Express your answer in simplest radical form.
The greatest distance = the body diagonal of the cube
8 = sqrt ( s^2 + s^2 + s^2)
8 = sqrt (3 s^2)
8 = s sqrt (3)
s = 8 /sqrt (3)
Volume = side^3 = (8/sqrt (3))^3 = [(512) / 3] / sqrt 3 = ( 512sqrt(3) / 9 ) in^3
