Find :

(i) the volume

(ii) the total surface area

(iii) the lateral surface area and

(iv) the length of the diagonal of a cube of side 10 cm.

Let 'a' be the side of a cube.

(i) Volume of cube = (a)³

= (10)³

= 1000 cm³.

Hence, volume = 1000 cm³.

(ii) By formula,

Total surface area of cube = 6a²

= 6 × 10²

= 600 cm².

Hence, total surface area of cube = 600 cm².

(iii) By formula,

Lateral surface area of cube = 4a²

= 4 × 10²

= 400 cm².

Hence, lateral surface area of cube = 400 cm².

(iv) By formula,

Diagonal of cube = $a\sqrt{3}$

= $10\sqrt{3}$

= 10 × 1.732

= 17.32 cm.

Hence, diagonal of cube = 17.32 cm.