Three metal cubes with 9, 12, and 15 cm edges are melted into a new cube. Find its edge.
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Answer: D. 18 cm
Explanation
Calculating the volume of each metal cube involves cubing their respective edge lengths of 9, 12, and 15 centimeters. Summing these individual volumes together gives a total combined volume of 5832 cubic centimeters. Taking the cube root of the total volume yields an edge length of 18 centimeters for the new melted cube. The volume of any geometric cube is calculated by raising the length of its edge to the third power. Melting solid objects preserves total volume, meaning the sum of individual volumes equals the new consolidated volume. The cube root operation reverses the cubing process to determine the linear edge length from a known volume.
Option A overestimates the new edge length by incorrectly adding linear dimensions instead of volumetric capacities. Option B represents an intermediate calculation error during the cube root evaluation step. Option C assumes an excessively large edge length that would yield a volume far greater than the combined sum.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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