Find the length of the diagonal of a closed cube whose total surface area is 96 m².

$4 \sqrt{3}$ m

We know that,

Diagonal of cube = \(\sqrt {3}\) × Side of cube

The total surface area of a cube = 6a² ( If a is the side )

We have,

The total surface area of the room = 96 m²

6a² = 96

= a² = 16

= a = 4

The length of the diagonal of the cube = 4\(\sqrt {3}\) m.