The greatest distance between two points on a cube is the distance between a vertex on one surface and the diagonally opposite vertex on the parallel surface. If you visualize a sphere circumscribing this cube, then this distance is the diameter of the sphere.

If I remember correctly, the radius of this sphere is s*(sqrt3)/2 where s is the side of the cube. So, diameter = s*sqrt3 and from (2), this is 3sqrt2.

So, you can find the volume. Hence sufficient.


However, one doubt I have in my mind is that if each of the statements in DS is sufficient then the calculations should yield the same answers for each of the statement. In this case, from statement (1), we can deduce that side of cube = 3. However, from statement (2), the side of cube would be three if the greatest distance would be 3(sqrt3) [and not 3sqrt2 as you mentioned.] Can you please verify it from the source of the question?

It may just be that I am doing the calculation of the radius of that sphere wrong.

Yes, you're right -- statement (2) should've been 3SQRT3.

Thanks for the explanations.