If the diagonal of a cube is 8√3 cm then the volume of cube is:

The correct answer is Option (4) → 512 cm³

The diagonal of a cube of side \(a\) runs from one corner to the opposite corner through the inside of the cube. By Pythagoras’ theorem its square is \(a^{2}+a^{2}+a^{2}=3a^{2}\), so its length is \(a\sqrt{3}\). The side follows from the diagonal, and the volume from the side.

• Side of the cube: \(a\sqrt{3}=8\sqrt{3}\), so \(a=8\) cm

• Volume, the cube of the side: \(a^{3}=8^{3}=512\,\mathrm{cm^3}\)