Scale Drawing

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In order to access this I need to be confident with:

Place value Decimals Ratio scale Enlargement Metric units

This topic is relevant for:

GCSE Maths Ratio and Proportion Scale

Scale Drawing

Here we will learn about scale drawings, including creating scale drawings, using scale factors, and word problems.

There are also scale diagrams and drawings worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is a scale drawing?

A scale drawing is an enlargement of an object.

An enlargement changes the size of an object by multiplying each of the lengths by a scale factor to make it larger or smaller.

The scale of a drawing is usually stated as a ratio.

E.g.

1cm:5m

This is said as “ $1$ centimetres to $5$ metres” and means every $1$ centimetre on the diagram represents $5$ metres in real life.

In order to interpret and produce scale drawings we need to know the scale factor and the actual lengths of the object.

E.g.

Below is a scale drawing of a pool with a scale of $\bf{1cm:2m}$ or $1:200.$

This means that every centimetre on the diagram represents $2$ metres in real life.

So the 6cm width of the diagram represents a $12m$ width on the real pool.

The real pool has been been enlarged by a scale factor of $\frac{1}{200}$ to give the scale drawing.

The majority of scale drawing questions will involve polygons or 2D drawings such as floor plans or using a map although there is overlap with topics such as enlargement, construction of triangles, and loci.

What is a scale drawing?

How to calculate the actual / real life distance from a scale

In order to calculate the actual/real life distance from a scale:

State the scale of the enlargement as a ratio in the form $\bf{1:n}$ .
Multiply $\bf{n}$ by the length given from the scale drawing.
Write the units.

Explain how to calculate the actual / real life distance from a scale

Scale drawing worksheet

Get your free scale drawing worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Scale drawing worksheet

Get your free scale drawing worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE

Related lessons on scale

Scale drawing is part of our series of lessons to support revision on scale. You may find it helpful to start with the main scale lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

Scale drawing examples

Example 1: map

A map has a scale of $1cm:2km.$ Find the actual distance represented by $5cm$ on the map.

State the scale of the enlargement as a ratio in the form $\bf{1:n}$ .

1cm:2km

2Multiply $\bf{n}$ by the length given from the scale drawing.

2 \times 5=10

3Write the units.

10km.

Example 2: plan of a building

A plan of a block of flats has the scale $2.5cm:800m.$ What is the real distance represented by $5.7cm$ on the plan?

State the scale of the enlargement as a ratio in the form $\bf{1:n}$ .

Dividing both sides by $2.5,$ we get $1cm:320m$

Multiply $\bf{n}$ by the length given from the scale drawing.

320 \times 5.7=1 \ 824

Write the units.

1 \ 824m

Example 3: atlas

A world atlas has a scale of $2cm:5 \ 000km.$ Calculate the real world distance that is represented by $23mm$ on the atlas.

State the scale of the enlargement as a ratio in the form $\bf{1:n}$ .

As the length required is in millimetres, we first need to change the $2cm$ to millimetres.

$2cm:5 \ 000km = 20mm:5 \ 000km$

The we can reduce the ratio so we have $1 \ mm:n \ km.$ Dividing both sides by $20,$ we get:

$1mm:250km$

Multiply $\bf{n}$ by the length given from the scale drawing.

250 \times 23=5750

Write the units.

5750km

How to calculate the scale drawing distance from a scale

In order to calculate the scale drawing distance from a scale:

State the scale of the enlargement as a ratio in the form $\bf{1:n}$ .
Divide the real life distance by the scale ratio.
Write the units.

Calculate scale drawing distance examples

Example 4: model object

A model car is made using the model to an actual distance of $1cm:40cm.$ The height of the car is $170cm.$ Calculate the height of the model car.

State the scale of the enlargement as a ratio in the form $\bf{1:n}$ .

The ratio given is $1:40$

Divide the real life distance by the scale ratio.

170 \div 40=4.25

Write the units.

4.25cm

Example 5: floor plan

A plan of a kitchen uses the scale $1cm:0.2m.$ Calculate the distance on the plan for the actual distance of $5.62m.$

State the scale of the enlargement as a ratio in the form $\bf{1:n}$ .

The ratio is already in the form $1:n$ .

$1cm:0.2m$

Divide the real life distance by the scale ratio.

5.62 \div 0.2=28.1

Write the units.

28.1cm

Example 6: map of the UK

A map of the UK is drawn using the scale $50cm:1400km.$ Calculate how far $86.8km$ would be on the map.

State the scale of the enlargement as a ratio in the form $\bf{1:n}$ .

Let’s convert the ratio to the form $1 \ cm:n \ km$ by dividing both sides of the ratio by $50.$

$50cm:1400km=1cm:28km$

Divide the real life distance by the scale ratio.

Now we can calculate the length on the map

$86.8 \div 28=3.1$

Write the units.

3.1cm

Common misconceptions

Multiplying the real life distance by the ratio scale

The real life distance is multiplied by the ratio scale, giving an incorrect distance on the plan.

Dividing the model / plan / map distance by the ratio scale

The distance on the model / plan / map is divided by the ratio scale meaning that the real life distance is incorrect.

Ratio scale not simplified

If given the ratio $2cm:5km,$ it is easier to calculate when the ratio is in the form $1:n$ and so we must find an equivalent ratio before using the scale.

Here the ratio would be $1cm:2.5km$ so $1cm$ on the map would be equal to $2.5km$ in real life.

Incorrect units in the solution

The units for the model are mixed up with the units for the real life distance. For example if we were calculating the distance of $10cm$ on a map with the scale ratio of $1cm:5km, \ 10 \times 5=50cm$ is stated whereas the correct solution would be $10 \times 5=50km.$

Converting units

Sometimes the units need to be converted so that you are working with the same units, making calculations much easier to comprehend. Make sure you know how to convert between different metric units. For example, the map scale is given as $1:25 \ 000$ which means that $1cm$ on the map is equivalent to $25 \ 000cm$ in real life.

If the answer is asked to be written in kilometres, the real life value in centimetres must be divided by $100 \ 000$ to get the same measurement in kilometres. $1:25 \ 000 = 1cm:0.25km$

Practice scale drawing questions

0.86km

0.86cm

10.5km

10.5cm

3 \times 3.5=10.5km

3750km

7500km

33.3km

3750cm

\begin{aligned} &2cm:500km = 1cm:250km \\\\ &250 \times 15=3750km \end{aligned}

10.738m

10.738cm

107.38m

3.08m

\begin{aligned} &1cm:1.82m \\\\ &1.82 \times 5.9=10.738m \end{aligned}

0.38864cm

0.38864m

4.96cm

4.96m

\begin{aligned} &138.8cm=1.388m \\\\ &10cm:2.8m=1cm:0.28m \\\\ &1.388 \div 0.28=4.96cm \end{aligned}

1.326m

13.26m

0.754km

0.754m

\begin{aligned} &8m:1400km=1m:175km \\\\ &132 \div 175=0.754m \ (3dp) \end{aligned}

28cm

6.22m

6.22cm

25.2cm

0.9cm:20cm=1cm:22.\dot{2}cm

Model to actual ratio is therefore $1cm:22.\dot{2}cm$

\begin{aligned} &5.6m=560cm \\\\ &560 \div 22. \dot{2}=25.2cm \end{aligned}

Scale drawing GCSE questions

1. A map has a scale of $1cm:0.5km.$ A dog walker walks around $18km$ per day. Calculate how far they will have walked on a map.

(2 marks)

Show answer

18 \div 0.5

(1)

=36cm

(1)

2. (a) The distance between two cities in an American State is $146.8km.$ The distance between the two cities on a map is $29.36cm.$ Calculate the scale ratio of the map to the actual distance in the form $1cm:nkm.$

(b) The river that travels through the state is measured on the plan to be $45cm.$ Calculate the actual length of the river. State the units in your solution.

(4 marks)

Show answer

(a)

146.8 \div 29.36=

(1)

1cm:5km

(1)

(b)

45 \times 5=225

(1)

km

(1)

3. Below is the map of a desert island.

Scale Drawing GCSE Question 3

Using the scale provided, calculate the distance between the Palm Trees and the Waterfall.

(3 marks)

Show answer

Distance $[6.3-6.7cm]$

(1)

Their $6.5 \times 50$

(1)

325m

(1)

Learning checklist

You have now learned how to:

Multiplying and dividing by powers of

10

in scale drawings or by multiplying and dividing by powers of a

1,000

in converting between units such as kilometres and metres

Solve problems involving similar shapes where the scale factor is known or can be found

The next lessons are

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