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Density: Question 2

Syllabus 1.4

Structured Core 4 marks

A student is investigating a rectangular metal block for a science project.

(a) The block measures 4.0 cm4.0\text{ cm} by 5.0 cm5.0\text{ cm} by 2.0 cm2.0\text{ cm}. Calculate the volume of the block. [1]

(b) The block has a mass of 168 g168\text{ g}. Calculate the density of the metal, giving your answer in g/cm3\text{g/cm}^3. [2]

(c) The density of aluminium is 2.7 g/cm32.7\text{ g/cm}^3. State, with a reason, whether the block could be made of aluminium. [1]

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Worked solution

Part (a): Volume of the cuboid

For a rectangular block, volume is length ×\times width ×\times height:

V=4.0×5.0×2.0V = 4.0 \times 5.0 \times 2.0

V=40 cm3V = 40\text{ cm}^3

Part (b): Density of the metal

Use the density formula with the mass and the volume just found:

ρ=mV=168 g40 cm3\rho = \frac{m}{V} = \frac{168\text{ g}}{40\text{ cm}^3}

ρ=4.2 g/cm3\rho = 4.2\text{ g/cm}^3

Part (c): Could the block be aluminium?

Compare the calculated density with the density of aluminium:

4.2 g/cm3≫2.7 g/cm34.2\text{ g/cm}^3 \gg 2.7\text{ g/cm}^3

The block’s density is much larger than that of aluminium, so the block cannot be made of aluminium. It must be a denser metal instead.

Final answers

  • (a) Volume == 40 cm340\text{ cm}^3
  • (b) Density == 4.2 g/cm34.2\text{ g/cm}^3
  • (c) No. The block is too dense to be aluminium.