The lateral surface area of cube is $256m^2$. Find its volume.

Step 1: Find the edge of the cube.

The lateral surface area of cube $=256m^2$

Let us consider $a$ as the edge of the cube.

The lateral surface area of a cube $=4a^2$

$$\begin{gathered} \Rightarrow 256=4a^2 \\ \Rightarrow a^2=256/4 \\ \Rightarrow a^2=64 \\ \Rightarrow a=8m \end{gathered}$$

Step 2: Find the volume of the cube.

The volume of the cube $=a^3=8^3=512m^3$

Hence, The volume of the cube is $512m^3$.