The diagonal of a cube is 6√3 cm. Its surface area and volume are:

The correct answer is Option (4) → 216 cm² and 216 cm³

The diagonal of a cube of edge \(a\) runs from one corner to the opposite corner through the inside, and its length is \(\sqrt{a^{2}+a^{2}+a^{2}}=a\sqrt{3}\).

• Edge of the cube: \(a\sqrt{3}=6\sqrt{3}\), so \(a=6\,\mathrm{cm}\)

• Surface area of the six square faces \(=6a^{2}=6\times36=\) 216 cm²

• Volume of the cube, the edge multiplied by itself three times, \(=a^{3}=6^{3}=\) 216 cm³