A cube of an unknown metal measures 1.61 mm on one side. The mass of the cube is 11.3 mg. Which of the following is most likely the unknown metal?

Question

BlackTom AI · Accepted Answer

A metal cube is given with side length 1.61 mm and mass 11.3 mg. To compare metals, we can estimate density from mass divided by volume.
First, compute the volume of the cube: V = (1.61 mm)^3 ≈ 4.173 mm^3. This is equivalent to 4.173 × 10^-3 cm^3 since 1 cm^3 = 1000 mm^3.
Next, convert the mass to grams: 11.3 mg = 0.0113 g.
Now determine the density: density ≈ mass / volume ≈ 0.0113 g / 0.004173 cm^3 ≈ 2.71 g/cm^3.
With the density in mind, compare the options to common metal densities:
Option 1 – rhodium: rhodium has a density around 12.4 g/cm^3, much higher than our calculated value, so this is unlikely.
Option 2 – copper: copper density is about 8.96 g/cm^3, significantly higher than 2.71 g/cm^3, making it an unlikely match.
Option 3 – vanadium: vanadium density is near 6.0 g/cm^3, still well above the estimated 2.71 g/cm^3, so this is not a good fit.
Option 4 – aluminum: aluminum has a well-known density around 2.70 g/cm^3, which closely matches our calculated value, making it the most plausible.
Option 5 – zirconium: zirconium density is about 6.5 g/cm^3, again far from 2.71 g/cm^3, so this option is unlikely.
The reasoning hinges on the density comparison: the calculated density aligns best with aluminum, while the other metals have notably higher densities that do not fit the measurement. The approach highlights how density serves as a discriminant among metals with similar appearance but different masses per volume.

A cube of an unknown metal measures 1.61 mm on one side. The mass of the cube is 11.3 mg. Which of the following is most likely the unknown metal? 单项选择题

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