The volume of a cube is 3375 cm³. What is the length of the longest rod that can be placed in this cube?

15$\sqrt{3}$ cm

We know that,

The volume of cube = side³

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

We have,

The volume of cube = 3375 cm³

= side³ = 3375 cm³

= side = 15 cm

length of the longest rod = \(\sqrt {3}\) × Side of cube = 15\(\sqrt {3}\) cm