A solid cube each of whose face diagonals is $128\sqrt{2}$cm, is moulded to make a cuboid. The length and the breadth of the cuboid are 512 cm and 160 cm respectively. What is the height of the cuboid?

25.6 cm

We have,

Volume of cube = (side)³

The volume of a cubiod = L × B × H

We have,

Diagonal of the face of a cube = 128\(\sqrt {2}\)

Diagonal of face of cube = side \(\sqrt {2}\)

128\(\sqrt {2}\) = \(\sqrt {2}\) × side

side = 128 cm

So,  Volume of the cube = (128)³

According to the question,

= (128)³ = L × B × H

= (128)³ = 512 × 160 × H

= H = 25.6 cm