P isthe center of one face of a cube and Q isthe center ofthe opposite face Ifthe length of the shortest possible path from P to Q alongthe outer surface ofthe cube is 2radic2 centi what's vol of cube?

The shortest path from P to Q along the surface of the cube will be one that goes from P, to the center point on any edge, to the opposite side, and then to Q. The length of that will be L + L/2 + L/2, or 2L, where L is the length of any side of the cube.

We are told that this distance is equal to 2√2, so we can say:

2L = 2√2 cm

∴ L = √2 cm

The volume of the cube will be that length, cubed, or L3, which means we can say:

V = L3

∴ V = (√2 cm)3

∴ V = (21/2)3 cm3

∴ V = 23/2 cm3