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?
Answer & explanation
Correct answer: option 1
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