Density Mass and Volume Problems
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Density Mass and Volume Problems — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionApplying 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

2QuestionCalculating Unknowns in the Density FormulaAssessment Practice
4 marks~6 minCriterion A
A materials engineer is identifying two unknown metals using a mass–volume graph. Line X passes through (0,0)(0, 0) and (10 cm3, 27 g)(10 \ \text{cm}^3, \ 27 \ \text{g}). Line Y passes through (0,0)(0, 0) and (10 cm3, 89 g)(10 \ \text{cm}^3, \ 89 \ \text{g}).
a
Explain how the gradient of each line gives the density of the material. [1]
b
Calculate the density of material X and the density of material Y. [2]
c
A component requires a metal with density greater than 8.0 g/cm38.0 \ \text{g/cm}^3. The engineer has 15 cm315 \ \text{cm}^3 of material Y available. Justify whether material Y should be selected for this component, and determine the mass of the component that could be made. [1]
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3QuestionChanging Units in Density ProblemsAssessment Practice
6 marks~9 minCriterion B
A materials engineer is selecting a foam for a buoyancy device. The foam must have a density below 750 kg/m3750 \ \text{kg/m}^3 to float with sufficient clearance.

Density data for four substances:

Density in g/cm3\text{g/cm}^3: 0.5, 1.0, 2.7, 8.90.5, \ 1.0, \ 2.7, \ 8.9

Density in kg/m3\text{kg/m}^3: 500, 1000, 2700, 8900500, \ 1000, \ 2700, \ 8900
a
Deduce the conversion factor from g/cm3\text{g/cm}^3 to kg/m3\text{kg/m}^3. [2]
b
Construct a general formula that converts a density dd in g/cm3\text{g/cm}^3 to density DD in kg/m3\text{kg/m}^3. [2]
c
The foam has a density of 0.72 g/cm30.72 \ \text{g/cm}^3. Use your formula to find its density in kg/m3\text{kg/m}^3, then advise the engineer whether this foam should be selected for the buoyancy device. [2]

Solutions

4QuestionMulti-Step Problems with Density and VolumeAssessment Practice
6 marks~9 minCriterion D
An aerospace engineer designs a lightweight alloy by combining Metal A (density 2.70 g/cm32.70 \text{ g/cm}^3) and Metal B (density 8.96 g/cm38.96 \text{ g/cm}^3). The finished component has a volume of 500 cm3500 \text{ cm}^3 and a target density of 4.50 g/cm34.50 \text{ g/cm}^3. Assume perfect mixing with no voids or impurities.
a
Calculate the mass of Metal A and the mass of Metal B required to achieve the target density. [4]
b
Identify and explain two limitations of the assumptions used in this model. [1]
c
The finished component is measured and found to have a volume of 495 cm3495 \text{ cm}^3 instead of 500 cm3500 \text{ cm}^3, while the total mass remains unchanged. Calculate the actual density of the component and advise the engineer whether the component should be accepted or rejected for use in the aircraft. [1]
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