Question

If the length of diagonal of a cube is $8\sqrt{3}\mathrm{cm}$, then its surface area is
(a) 192 cm²
(b) 384 cm²
(c) 512 cm²
(d) 768 cm²

Answer 1

(b) 384 cm²
We have:
$$\begin{gathered} \sqrt{3}a=8\sqrt{3} \\ \Rightarrow a=8\mathrm{cm} \end{gathered}$$

∴ Surface area of the cube = $6a^2=6\times 8\times 8=384{\mathrm{cm}}^2$