Density Mass and Volume Problems
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Density Mass and Volume Problems — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionChanging Units in Density ProblemsConcept Practice
2 marks~3 minCriterion B
The density of three substances is given in two unit systems.

Water: 1.00 g/cm31.00 \ \text{g/cm}^3 and 1000 kg/m31000 \ \text{kg/m}^3
Aluminium: 2.70 g/cm32.70 \ \text{g/cm}^3 and 2700 kg/m32700 \ \text{kg/m}^3
Lead: 11.3 g/cm311.3 \ \text{g/cm}^3 and 11300 kg/m311300 \ \text{kg/m}^3
a
Deduce the relationship between a density value expressed in g/cm3\text{g/cm}^3 and the same density expressed in kg/m3\text{kg/m}^3. [1]
b
A sample of iron has a density of 7.87 g/cm37.87 \ \text{g/cm}^3. Justify whether this density is greater or less than 8000 kg/m38000 \ \text{kg/m}^3. [1]

Solutions

2QuestionMulti-Step Problems with Density and VolumeAssessment Practice
2 marks~3 minCriterion D
A jeweller melts 50 g of gold (density 19.3 g/cm³) and 30 g of silver (density 10.5 g/cm³) to produce an alloy ring.
a
Calculate the total volume of the alloy. [1]
b
The jeweller claims the alloy ring qualifies for hallmarking as a "high-density gold alloy," which requires a minimum density of 15.0 g/cm³. Using your result from part (a), determine the density of the alloy and advise the jeweller whether the ring meets this requirement. [1]
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Solutions

3QuestionMulti-Step Problems with Density and VolumeConcept Practice
2 marks~3 minCriterion A
A manufacturer produces solid aluminium blocks for industrial shelving. Each block is a rectangular prism with length 8 cm, width 5 cm, and an unlabelled height. The density of aluminium is 2.5 g/cm32.5 \text{ g/cm}^3 and each block has a mass of 300 g.

A storage shelf has a maximum load of 250 g per block.
a
Calculate the height of the block. [1]
b
Advise the manufacturer whether this block is suitable for the shelf. Justify your answer. [1]
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Solutions

4QuestionApplying Density to Real-World SituationsAssessment Practice
4 marks~6 minCriterion C
A materials scientist measures the mass and volume of samples of an unknown alloy. The graph shows a straight line through the origin and the point (2,8)(2, 8), where the horizontal axis represents volume (m3\text{m}^3) and the vertical axis represents mass (kg\text{kg}).
a
Explain how the gradient of this graph represents the density of the alloy. [1]
b
Calculate the density of the alloy. [1]
c
Titanium alloys used in aerospace components must have a density below 5 kg/m35 \ \text{kg/m}^3 to meet structural weight limits. Advise whether this alloy should be approved for use in aerospace structural components, justifying your answer with reference to the density threshold. [2]
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Solutions

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