A rectangular block of an unknown metal has dimensions length = 5.0 cm, breadth = 3.0 cm, height = 2.0 cm and mass = 210 g. Calculate its density and state whether the metal could be aluminium (density of aluminium = 2.70 g cm⁻³).

medium 3 marks Class 10 · Science · Metals and Non-metals

Answer

Density = 7.0 g cm⁻³; the metal cannot be aluminium.

The correct answer is Density = 7.0 g cm⁻³; the metal cannot be aluminium. — State the density and the conclusion.

Step-by-step solution

Find the volume of the block using $V = length \times breadth \times height$ .
Substitute the given values: $V = 5.0 \times 3.0 \times 2.0 = 30.0 cm^{3}$ .
Density $ρ$ is mass divided by volume: $ρ = \frac{m}{V}$ .
Insert the mass: $\rho = \frac{210\,\text{g}}{30.0\,\text{cm}^3 = 7.0\,\text{g cm}^{-3}$ .
Compare with aluminium’s density (2.70 g cm⁻³). Since 7.0 > 2.70, the metal cannot be aluminium.
State the density and the conclusion.

Common mistake: Using the volume of a cube instead of the given rectangular dimensions.

Concept tested: Density calculation and identification of metal