Three iron cubes have edges of 6 cm, 8 cm, and 10 cm. Melted together into a new cube, find its edge.
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Answer: B. 12 cm
Explanation
The volume of each individual metal cube is calculated by cubing its edge length. Summing the three individual volumes gives a combined total volume of seventeen hundred twenty eight. Taking the cube root of the total volume determines the edge length of the new cube as twelve centimeters. The volume of any cube equals its edge length raised to the third power. Melting and recasting metal objects preserves the total volume of the material involved. Cube roots reverse the cubing operation to find linear edge dimensions from total volumes.
Foundries and metalworking industries rely on volume conservation principles when recasting metal parts. Sculptors and manufacturers calculate material requirements using three dimensional volumetric scaling. Geometric volume problems demonstrate the physical conservation of mass and space in containers. Option a matches the edge of one of the smaller original cubes rather than the new combined cube. Option c overestimates the new edge length by miscalculating the total volume sum. Option d matches the largest original cube edge instead of the newly formed solid.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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