Converting between other compound measures | Maths | Quizalize & Oak National Academy

Starter quiz

What is volume?

The amount of space occupied by an open 3D shape.

The amount of space occupied by a closed 2D shape.

The amount of space occupied by a closed 3D shape. ✓

The amount of space occupied by an open 3D shape.

Space
A square has a length of 12 cm. What is this length in mm?

120 mm ✓

1200 mm

0.12 mm

1.2 mm
A square has lengths 12 m. What is this length in cm?

120 000 cm

1.2 cm

120 m

1200 cm ✓
Match the volumes with the following cubes or cuboids.

27 cm $^3$

⇔

A 3 cm by 3 cm by 3 cm cube. ✓

8 cm $^3$

⇔

A 2 cm by 2 cm by 2 cm cube. ✓

1 000 cm $^3$

⇔

A 10 cm by 10 cm by 10 cm cube. ✓

6 cm $^3$

⇔

A 1 cm by 2 cm by 3 cm cuboid. ✓

9 cm $^3$

⇔

A 2 cm by 4.5 cm by 1 cm cuboid. ✓
Match the lengths of the cubes with the volume.

Cube with length 4 cm

⇔

Volume of cube = 64 cm $^3$ ✓

Cube with length 3 cm

⇔

Volume of cube = 27 cm $^3$ ✓

Cube with length 5 cm

⇔

Volume of cube = 125 cm $^3$ ✓

Cube with length 1 mm

⇔

Volume of cube = 1 mm $^3$ ✓

Cube with length 4 mm

⇔

Volume of cube = 64 mm $^3$ ✓
If the volume of a cube is given as the expression 27 $x^3$ . What is the length of the cube in terms of $x$ ?

'3x' ✓

Exit quiz

The length of a square is 4 cm. Work out the area of the square in mm.

16 cm $^2$

160 mm $^2$

1600 mm $^2$ ✓

16 000 mm $^2$
Match the equivalent areas with the different units of measure.

2 cm $^2$

⇔

200 mm $^2$ ✓

2 m $^2$

⇔

20 000 cm $^2$ ✓

2 km $^2$

⇔

2 000 000 m $^2$ ✓

2 000 000 mm $^2$

⇔

2 m $^2$ ✓
Match the equivalent volumes with the different units of measure.

6 cm $^3$

⇔

6 000 mm $^3$ ✓

6 000 000 cm $^3$

⇔

6 m $^3$ ✓

6 km $^3$

⇔

6 000 000 000 m $^3$ ✓

60 cm $^3$

⇔

60 000 mm $^3$ ✓

6 m $^3$

⇔

6 000 000 000 mm $^3$ ✓
Put the following in order of density, put the cube with the biggest density at the top.

1

⇔

Cube Z has a mass = 9 kg and a volume of 360 cm $^3$

2

⇔

Cube W has a mass = 3.5 kg and a volume = 700 cm $^3$

3

⇔

Cube X has a mass = 4 g and a volume = 0.05 m $^3$

4

⇔

Cube Y has a mass = 2000 g and a volume = 80 000 cm $^3$
There are two cubes with the same mass, but different lengths. Cube A has lengths 4 cm and Cube B has lengths 8 cm. Which of the following is true?

The densities are the same because the masses are the same.

The density of Cube B will be half the density of Cube A.

The density of Cube A will be half the density of Cube B.

The density of Cube A will be 8 times the density of Cube B. ✓

The density of Cube B will be 8 times the density of Cube A.
A box has density given a mass of $M$ kg and a volume $V$ m $^3$ . The same box has a pressure as a result of a force of $N$ newtons applied to an area of $A$ m $^2$ . Match the statements.

This doubles the density.

⇔

Mass = $M$ kg and the Volume = $\frac{1}{2} V$ m $^3$ ✓

This halves the density.

⇔

Mass = $M$ kg and the Volume = $2 V$ m $^3$ ✓

This quadruples the pressure.

⇔

Force = $4 N$ newtons is applied to an an Area = $A$ m $^2$ ✓

This quarters the pressure.

⇔

Force = $N$ newtons is applied to an an Area = $4A$ m $^3$ ✓

Worksheet

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Lesson Details

Key learning points

The units for density can be converted to alternative units.
The units for pressure can be converted to alternative units.

Common misconception

Pupils understand they multiply by 100 when converting m to cm, but when converting m^2 to cm^2, fail to recognise the need to multiply by 100^2. This is also the same with volume conversions.

Illustrate a 1m^2 square and the equivalent 100cm^2 square, calculating the area and allowing pupils to see the equivalence of 1 m^2 = 10 000 cm^2. Also apply this to a 1m^3 and 100cm^3, thus allowing students to see 1m^2 = 100 000 cm^3.

Keywords

Pressure - Pressure is the perpendicular force applied to the surface of an object per unit area over which that force is distributed.
Density - The density of a substance is measured as the substance's mass per unit of volume.