if the diagonal of a cube is √27 cm, then its volume is:

Given,

Diagonal of Cube  = √27

We know that,

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

Volume of Cube = Side³

= \(\sqrt {3}\) × Side of Cube = $\sqrt {3}$

= Side of Cube = \(\frac{3\sqrt {3}}{\sqrt {3}}\)

= Side of Cube = 3

Then the volume of a cube = 3³ = 27