Question

The lateral surface area of a cube is $256c{m}^2$. The volume of the cube is:

Answer 1

Given:
Lateral surface area of a cube $=256c{m}^2$

We know that, Lateral surface area of a cube $=4a^2$

$\Rightarrow 256=4a^2$

$\Rightarrow a^2=\frac{256}{4}$

$\Rightarrow a^2=64$

$\Rightarrow a=8cm$

$\therefore$ Volume of cube $=a^3$
$=(8{)}^3$
$=512c{m}^3$

Hence, the volume of the cube is $512c{m}^3$.