The length of the diagonal of a cube is $6\sqrt{6} \text{ cm}$. The total surface area of the cube is :

1. 216 cm²

2. 432 cm²

3. 1296 cm²

4. 1548 cm²

Given,

Length of the diagonal of a cube = $6\sqrt{6}$ cm

Calculating the side of a cube,

Diagonal of a cube = $a\sqrt{3}$

⇒ $6\sqrt{6} = a\sqrt{3}$

⇒ a = $\dfrac{6\sqrt{6}}{\sqrt{3}}$

⇒ a = $6\sqrt{2}$ cm.

Calculating the total surface area of a cube,

Total surface area of a cube = 6a²

= 6 × $(6\sqrt{2})^2$

= 6 × 36 × 2

= 432 cm².

Hence, option 2 is the correct option.