Three metal cubes with edges of 3 dm, 4 dm, and 5 dm are melted into a single cube. Find the new edge.
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Answer: D. 6 dm
Explanation
The volume of each metal cube is found by cubing its respective decimeter edge length. Adding the individual volumes together gives a cumulative total volume of two hundred sixteen cubic decimeters. Taking the cube root of two hundred sixteen determines the new edge length as six decimeters. Decimeters are metric units of length where one cubic decimeter equals one liter of volume. The volume conservation principle applies when multiple solid objects are melted into a single shape. Cube roots calculate linear side dimensions directly from three dimensional volumetric measurements.
Metallurgy and casting processes require precise volume calculations to ensure proper mold filling. Metric unit conversions are essential in scientific and industrial manufacturing applications. Volume scaling exercises reinforce spatial visualization and geometric formula comprehension. Option a matches the edge of the smallest original cube rather than the combined solid. Option b corresponds to the medium sized original cube instead of the final melted product. Option c matches the largest original cube edge rather than the total volume outcome.
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- Mathematics
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- Mathematics
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