Find the volume of a cube whose diagonal length is \(18\sqrt{3}\) cm.

Solution:

For a cube, diagonal $d = a\sqrt{3}$

Given:
$d = 18\sqrt{3}$

So,
$a\sqrt{3} = 18\sqrt{3}$

$\Rightarrow a = 18$ cm

Volume of cube:
$a^3 = 18^3 = 5832\ \text{cm}^3$

✅ Final Answer: 5832 cm³