The square on the diagonal of a cube has an area of 1875 cm². Calculate :

(i) the side of the cube,

(ii) the surface area of the cube.

(i) Given,

Area = 1875 cm².

We know that,

Diagonal of cube (d) = $\sqrt{3}$ a

The square on the diagonal means a square whose side is equal to the diagonal of the cube.

∴ Area of square = (diagonal)²

⇒ 1875 = (a $\sqrt{3})$²

⇒ 1875 = 3a²

⇒ a² = $\dfrac{1875}{3}$

⇒ a² = 625

⇒ a = $\sqrt{625}$

⇒ a = 25 cm.

Hence, side of cube = 25 cm.

(ii) Given,

Total surface area of cube = 6a².

= 6 × (25)²

= 6 × 625

= 3750 cm².

Hence, surface area of the cube = 3750 cm².