Find the volume of a cubical box whose surface area is 486 cm².

Let a be the length of cubical box.

Surface area of cubical box = 6a²

$6a^2 = 486\\[1em] ⇒ a^2 = \dfrac{486}{6}\\[1em] ⇒ a^2 = 81\\[1em] ⇒ a = \sqrt{81}\\[1em] ⇒ a = 9$

Volume of cubical box = $a^3$

$(9)^3\\[1em] = 9 \times 9 \times 9\\[1em] = 729$

The volume of cubical box is 729 cm³.