If the volume of a cube is 27 cm3, then the diagonal of the cube is

The correct answer is Option (2) → \(3\sqrt{3}\) cm

The volume of a cube of side \(a\) is \(a^3\), and its diagonal (from one corner to the opposite corner through the inside) is \(a\sqrt{3}\), because it is the hypotenuse of a right triangle whose sides are an edge \(a\) and a face diagonal \(a\sqrt{2}\).

• \(a^3=27\), so \(a=3\) cm

• Diagonal \(=a\sqrt{3}=3\sqrt{3}\) cm