Density Mass and Volume Problems
You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 84 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

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

1QuestionChanging Units in Density ProblemsAssessment Practice
4 marks~6 minCriterion C
A graph of mass (kg) against volume (m³) for a sample of aluminium produces a straight line through the origin. The gradient of the line is 2700 kg/m32700 \ \text{kg/m}^3.
a
State the conversion factors needed to change kg to g and m³ to cm³. [1]
b
Show that 1 kg/m3=0.001 g/cm31 \ \text{kg/m}^3 = 0.001 \ \text{g/cm}^3, and hence calculate the density of aluminium in g/cm³. [2]
c
A student claims that because the numerical value decreased from 2700 to 2.7, the density itself has decreased. Critique this claim. [1]
Question diagram

Solutions

2QuestionCalculating Unknowns in the Density FormulaAssessment Practice
4 marks~6 minCriterion D
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]
Question diagram

Solutions

3QuestionMulti-Step Problems with Density and VolumeAssessment Practice
4 marks~6 minCriterion A
A cylindrical rod is made by fusing a 12 cm aluminium section to an 8 cm brass section. Both sections have radius 1.5 cm. The density of aluminium is 2.70 g/cm³ and the density of brass is 8.50 g/cm³. An engineer requires the composite rod to have an overall density greater than 4.50 g/cm³ to meet a structural specification.
a
Calculate the total volume of the composite rod. [1]
b
Calculate the total mass of the composite rod. [2]
c
Advise the engineer whether the rod meets the structural specification, justifying your answer with the calculated overall density. [1]
Question diagram

Solutions

4QuestionChanging 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

Questions 5-88

Unlock these questions with Premium

Sign Up →

That's every free question here — 4 of 88.

+84 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade