Question

The lateral surface area of a cube is 256 cm². The volume of the cube is __________.

Answer 1

Let the edge of the cube be a cm.

Lateral surface area of cube = 256 cm² (Given)

$\Rightarrow 4a^2=256$

$\Rightarrow a^2=64$

$\Rightarrow a=8\mathrm{cm}$

∴ Volume of the cube = a³ = (8 cm)³ = 512 cm³

Thus, the volume of the cube is 512 cm³.

The lateral surface area of a cube is 256 cm². The volume of the cube is __512 cm³__.