Question

The lateral surface area of a cube is 256 m². The volume of the cube is
(a) 64 m³
(b) 216 m³
(c) 256 m³
(d) 512 m³

Answer 1

(d) 512 m³

Suppose that a m be the edge of the cube.
We have:
$$\begin{gathered} 4a^2=256 \\ \Rightarrow a^2=\frac{256}{4}=64 \\ \Rightarrow a=8\mathrm{m} \end{gathered}$$

∴ Volume of the cube = $a^3{\mathrm{m}}^3=8^3{\mathrm{m}}^3=512{\mathrm{m}}^3$