A rectangular bar of an unknown metal has length 40.0 cm, breadth 2.0 cm, height 1.5 cm and mass 540 g. Calculate its density and comment whether the metal could be copper (density = 8.96 g/cm³).
Answer
Density = 4.5 g/cm³; therefore it is not copper.
The correct answer is Density = 4.5 g/cm³; therefore it is not copper. — Compare with the density of copper (8.96 g/cm³). Since 4.5 g/cm³ ≠ 8.96 g/cm³, the metal cannot be copper.
Step-by-step solution
- Find the volume of the bar: V = length × breadth × height = 40.0 cm × 2.0 cm × 1.5 cm = 120.0 cm³.
- Calculate density: ρ = mass/volume = 540 g / 120.0 cm³ = 4.5 g/cm³.
- Compare with the density of copper (8.96 g/cm³). Since 4.5 g/cm³ ≠ 8.96 g/cm³, the metal cannot be copper.
Common mistake: Using mass/length instead of mass/volume, or forgetting to multiply all three dimensions for volume
Concept tested: Density calculation of metals
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