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 MYP4 Mathematics (Standard) Practice Questions

1QuestionUnderstanding the Density FormulaConcept Practice

2 marks~3 minCriterion A

A solid rectangular prism used in a materials science demonstration has a length of 8 cm, a width of 5 cm, and a height of 3 cm. Its mass is 360 g. A material is classified as a heavy-density solid if its density exceeds 2.5 g/cm³.

Calculate the density of the prism. [1]

Justify whether the prism qualifies as a heavy-density solid. [1]

Solutions

2QuestionChanging 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 \ \text{kg/m}^3

State the conversion factors needed to change kg to g and m³ to cm³. [1]

Show that

1 \ \text{kg/m}^3 = 0.001 \ \text{g/cm}^3

, and hence calculate the density of aluminium in g/cm³. [2]

A student claims that because the numerical value decreased from 2700 to 2.7, the density itself has decreased. Critique this claim. [1]

Solutions

3QuestionChanging Units in Density ProblemsConcept Practice

2 marks~3 minCriterion B

The density of three substances is given in two unit systems.

Water:

1.00 \ \text{g/cm}^3

and

1000 \ \text{kg/m}^3

Aluminium:

2.70 \ \text{g/cm}^3

and

2700 \ \text{kg/m}^3

Lead:

11.3 \ \text{g/cm}^3

and

11300 \ \text{kg/m}^3

Deduce the relationship between a density value expressed in

\text{g/cm}^3

and the same density expressed in

\text{kg/m}^3

. [1]

A sample of iron has a density of

7.87 \ \text{g/cm}^3

. Justify whether this density is greater or less than

8000 \ \text{kg/m}^3

. [1]

Solutions

4QuestionMulti-Step Problems with Density and VolumeAssessment Practice

4 marks~6 minCriterion D

A cargo shipping company uses the formula

\text{mass} = \text{density} \times \text{volume}

to estimate the total mass of mixed cargo loaded into a standard 20-foot container with an internal volume of

33.2 \text{ m}^3

. The cargo consists of 50 steel drums and 80 wooden crates. Each steel drum has a volume of

0.20 \text{ m}^3

and a density of

7800 \text{ kg/m}^3

. Each wooden crate has a volume of

0.25 \text{ m}^3

and a density of

600 \text{ kg/m}^3

Calculate the estimated total mass of the cargo. [2]

The company's safety regulations state that the total cargo mass must not exceed

95\,000 \text{ kg}

. Advise the shipping company whether the cargo should be cleared for loading, identifying one reason why the actual mass could differ from your estimate. [2]

Solutions

Questions 5-88

Unlock these questions with Premium

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

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

Upgrade