Final answer:
The length of each side of the smaller cubes formed after melting and reshaping the original iron cube is 2 cm.
Step-by-step explanation:
The student asked about the length of the side of smaller cubes after an iron cube is melted down and reformed into equal smaller cubes. The original cube with 8 cm sides is melted to form 64 smaller cubes.
To find out the length of each smaller cube, we calculate the volume of the original cube and then divide this volume by the number of smaller cubes to get the volume of each new cube.
Since cubes have equal sides, we can then find the cube root of the volume to get the length of each side.
The volume of the original cube is calculated using the formula for the volume of a cube:
- Volume = side ³ = 8 cm ³ = 512 cm³.
Divide this volume by the number of smaller cubes (64) to get the volume of each smaller cube:
- Volume of each smaller cube = 512 cm³ / 64 = 8 cm³.
Finally, take the cube root of the volume of each smaller cube to find the length of each side:
- Side length of each smaller cube = ∛(8 cm³) = 2 cm.
Therefore, the length of each side of the smaller cubes is 2 cm.