The density of a substance is measured as the substance's mass per unit of volume.

Combining densities

Maths

Checking and further securing understanding of direct proportion in context

Compound measures for speed

Compound measures for density

Compound measures for pressure

Converting between metric speed measures

Converting between metric and imperial speed measures

Combining speeds

Problem solving with compound measures

In this unit, pupils will be exploring the multiplicative relationship between different compound measures. Ratio will be one of the ways in which this is explored and the skills from the prior unit will aid understanding. There are also links to the volume units as volume is required for the density formula.

In this unit, pupils explore the multiplicative relationship between different compound meaures and units such as speed, rates of pay, density and pressure.

Compound measures

The alloy can provide greater resistance to corrosion.

Every alloy is more expensive than its parts. 

What are the benefits when combining metals to make an alloy compared to pure metals?

A block of metal A has a mass of 400 g and a volume of 50 cm$$^3$$. A block of metal B has a mass of 300 g and a volume of 75 cm$$^3$$. What is the combined density of the two metals?

Liquid X has a density of 1.2 g/cm$$^3$$ and a volume of 100 cm$$^3$$. Liquid Y has a density of 0.8 g/cm$$^3$$ and a volume of 150 cm$$^3$$. What is the combined density of liquid X and Y?

A piece of wood (density 0.5 g/cm$$^3$$, volume 100 cm$$^3$$) is glued to a piece of plastic (density 1.4 g/cm$$^3$$, volume 50 cm$$^3$$). What is the average density of the combined piece?

An alloy is made by combining 3 kg of metal K (density 5 g/cm$$^3$$) with 2 kg of metal L (density 3 g/cm$$^3$$). What is the density of the alloy in g/cm$$^3$$? Give your answer to 1 s.f in g/cm^3.

A tank contains 2 litres of oil (density 0.9 g/cm$$^3$$) and 3 litres of water (density 1 g/cm$$^3$$). What is the density of the mixture in kg/m$$^3$$?

The {{}} of a substance is measured as the substance's mass per unit of volume. 

A metal block has a mass of 600 grams and a volume of 200 cm$$^3$$. What is the density of the metal?

A rectangular block has a density of 2.5 g/cm$$^3$$, a length of 10 cm, a width of 4 cm, and a height of 5 cm. What is the mass of the block? Give your answer in g.

A cylinder has a radius of 3 cm, a height of 10 cm, and is made of a material with a density of 7.8 g/cm$$^3$$. What is the mass of the cylinder? Give the answer in g to the nearest integer. 

A piece of wood has a mass of 240 grams and a density of 0.6 g/cm³. What is the volume of the wood? Give your answer in cm$$^3$$.

Osmium has a mass = 22 600 kg and a volume = 1 m$$^3$$

Iridium has a mass = 1120 kg and a volume = 0.05 m$$^3$$

Platinum has a mass = 64.5 kg and a volume = 0.003 m$$^3$$

Gold has a mass = 1.93 kg and a volume = 0.0001 m$$^3$$

Silver has a mass = 21 000 kg and a volume = 2 m$$^3$$

Put the following densities in order, starting with the densest at the top.

Combining densities

Lesson outcome