Answer:
the length of each side of the cube is 156.79 mm.
Explanation:
To find the length of each side of the cube formed by melting the rectangular block of metal, we need to determine the volume of the rectangular block and then find the edge length of the cube with the same volume.
The volume of the rectangular block is given by:
Volume = length × width × height
Volume = 256 mm × 152 mm × 81 mm
Volume = 3,934,848 mm³
Now, since the cube has equal sides, we need to find the edge length (x) of the cube with the same volume:
Volume of the cube = x³
Setting the volumes equal to each other:
x³ = 3,934,848
Now, find the cube root of the volume to get the edge length of the cube:
x = ∛3,934,848
x ≈ 156.79 mm
Therefore, the length of each side of the cube is approximately 156.79 mm.