Question

The length of the diagonal of a cube is $6\sqrt{3}\mathrm{cm}$. Its total surface area is
(a) 144 cm²
(b) 216 cm²
(c) 180 cm²
(d) 108 cm²

Answer 1

(b) 216 cm²

Let the edge of the cube be a cm.
Then, length of the diagonal = $\sqrt{3}a$
Or,
$$\begin{gathered} \sqrt{3}a=6\sqrt{3} \\ \Rightarrow a=6\text{cm} \end{gathered}$$
Therefore, the total surface area of the cube = 6a²
$$\begin{gathered} =\left(6\times 6\times 6\right){\text{cm}}^3 \\ =216{\text{cm}}^3 \end{gathered}$$