The surface area of a cube is 1536 cm². Find :

(i) the length of its edge

(ii) its volume

(iii) the volume of its material whose thickness is 5 mm.

Let 'a' be the length of the edge (side of a cube).

(i) Total surface area of cube = 6a²

⇒ 1536 = 6a²

⇒ a² = $\dfrac{1536}{6}$

⇒ a² = 256

⇒ a = $\sqrt{256}$

⇒ a = 16 cm.

Hence, length of the edge = 16 cm.

(ii) By formula,

Volume of cube = a³

= 16³

= 4096 cm³.

Hence, volume of cube = 4096 cm³.

(iii) Material thickness = 5 mm = 0.5 cm

Outer edge = 16 cm

Inner edge = 16 - (0.5 + 0.5) = 16 - 1 = 15 cm.

Volume of the material = (outer edge)³ - (inner edge)³

= (16)³ - (15)³

= 4096 - 3375

= 721 cm³.

Hence, volume of the material = 721 cm³.