Three cubes of sides 5 cm, 4 cm and 3 cm are melted to form a new cube. Find the length of the diagonal of the new cube.

Question

Question

This question was previously asked in

SSC GD Constable (2022) Official Paper (Held On : 17 Jan 2023 Shift 4)

Answer 1

Given:

Side of cube1 = 5 cm

Side of cube2 = 4 cm

Side of cube3 = 3 cm

Concept:

Volume of a cube = Side³;

Diagonal of a cube = √3 × Side

Solution:

⇒ Volume of new cube = Volume of cube1 + Volume of cube2 + Volume of cube3

⇒ Volume of new cube = 5³ + 4³ + 3³

⇒ Volume of new cube = 125 + 64 + 27

⇒ Volume of new cube = 216 cm³

⇒ Side of new cube = ∛Volume of new cube

⇒ Side of new cube = ∛216

⇒ Side of new cube = 6 cm

⇒ Diagonal = √3 × Side

⇒ Diagonal = \(6 \sqrt{3}\) cm

Therefore, the length of the diagonal of the new cube is \(6 \sqrt{3}\) cm.