Question

The volume of a cube is 512 cm³. Its total surface area is
(a) 256 cm²
(b) 384 cm²
(c) 512 cm²
(d) 64 cm²

Answer 1

(b) 384 cm²

Suppose that a cm is the edge of the cube.
We have:
$$\begin{gathered} a^3=512 \\ \Rightarrow a=\sqrt[3]{512}=8\mathrm{cm} \end{gathered}$$

$$\begin{gathered} \therefore \mathrm{Total}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{cube}=6a^2{\mathrm{cm}}^2 \\ =6\times 8\times 8{\mathrm{cm}}^2=384{\mathrm{cm}}^2 \end{gathered}$$