Three metal cubes with edge lengths 3 m, 4 m, and 5 m are melted together and recast into a single cube. Find the edge length of the newly formed cube.

Introduction / Context:
This question tests volume conservation. When solid objects are melted and recast without loss of material, the total volume before melting equals the volume after casting. By adding the volumes of the three cubes and equating it to the volume of the new cube, the new edge length can be found.

Given Data / Assumptions:

• Edges of cubes = 3 m, 4 m, 5 m
• Volume of a cube = edge^3
• Total volume is conserved

Concept / Approach:
Calculate the individual volumes of the three cubes, sum them, and equate the total to the volume of the new cube. Take the cube root of the total volume to find the new edge length.

Step-by-Step Solution:
Volume1 = 3^3 = 27 m^3 Volume2 = 4^3 = 64 m^3 Volume3 = 5^3 = 125 m^3 Total volume = 27 + 64 + 125 = 216 m^3 Let new edge = a a^3 = 216 a = 6 m

Verification / Alternative check:
Since 6^3 = 216, the computed edge length exactly matches the total volume, confirming correctness.

Why Other Options Are Wrong:
15 m: sum of edges, not volume-based. 4 m and 9 m: cubes of these values do not equal 216. 12 m: cube is far larger than the combined volume.

Common Pitfalls:
Adding edges instead of volumes. Forgetting to take the cube root at the end. Arithmetic mistakes while summing volumes.

Final Answer:
Edge of the new cube = 6 m