# Convert Scale Diagrams to Real Measurements

In this worksheet, students will apply scale factors to find the real life values of specific scaled elements or calculate the scale which has been used to create a scale diagram or model.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change, Mensuration

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Units and Measurement

Difficulty level:

### QUESTION 1 of 10

A lot of the time, it's not really the best idea to have things full size.

A map would be useless if it was full size, and a toy car doesn't really want to be the same size as a normal car, does it?

When we have an issue like this in maths, we use a scale diagram or a scale model.

What Is a Scale Diagram / Model?

A scale diagram is just a diagram where everything has been reduced by the same factor

It could be half the size, a tenth of the size, or anything else, but every element must be reduced by exactly the same factor.

How Are Scales Written?

Scales are written as ratios, such as 1: 100 or 1:50,000.

What Does a Scale Mean?

Scales are read from left to right.

For example, the scale 1:100 would mean that every 1 unit of length on the scale is the same as 100 units in real life.

So an element that was 2 cm long on a scale diagram, would be 200 cm long in real life.

Let's look at this concept in action with some examples now.

e.g. A model car is 1.5 cm tall. If the scale used to create it is 1:100, how tall would the car be in real life?

All we need to do here is multiply by the scale factor:

1.5 × 100 = 150 cm

So the car would be 150 cm or 1.5 m tall in real life.

e.g. A model is made of a 2 m tall man. If the model is 4 cm tall, what scale has been used?

The first thing we should notice here is that the units used are different, so we need to make them the same before we start:

There are 100 cm in 1 m, so 2 m = 200 cm.

Now, we need to write these numbers as a ratio (remember that the model comes first):

4:200

Our final step is to simplify this ratio:

4:200 ÷ 4

1:50

In this activity, we will apply scale factors to find the real life scale values of specific scaled elements or calculate the scale which has been used to create a scale diagram or model.

A scale of 1:100 means that 1 cm on a model is 100 cm in real life.

When is this statement true?

Always

Sometimes

Never

A toy car has wheel that are 0.5 cm wide.

How wide are the real wheels if the model has been produced to a scale of 1:48?

Type your answer as a number below without any units, as these have already been provided for you.

Always

Sometimes

Never

A model railway is built to a scale of 1:500.

If the track is 2.3 m long, how long is the track in real life?

Type your answer as a number below without any units, as these have already been provided for you.

Always

Sometimes

Never

A model is made of a garden at a scale of 1:1000.

How tall are the real trees if the model is 1 cm high?

Type your answer as a number below without any units, as these have already been provided for you.

Always

Sometimes

Never

Match each pair of scale and real measurements on the left with the correct scale factor (expressed as a ratio) on the right.

## Column B

2 cm model; 10 cm real
1:12
0.3 cm model; 3 cm real
1:5
2 m model; 4 m real
1:2
10 cm model; 1.2 m real
1:10

A toy car is 2 cm long.

If the real car is 1.8 m long, what scale has been used to create the toy?

## Column B

2 cm model; 10 cm real
1:12
0.3 cm model; 3 cm real
1:5
2 m model; 4 m real
1:2
10 cm model; 1.2 m real
1:10

A 4 cm tall model building has been created using a scale of 1:750 in comparison with the real building.

How tall is the real building in metres?

Type your answer as a number below without any units, as these have already been provided for you.

## Column B

2 cm model; 10 cm real
1:12
0.3 cm model; 3 cm real
1:5
2 m model; 4 m real
1:2
10 cm model; 1.2 m real
1:10

Which of the measurements below have a scale factor of 1:200?

Select either 'Correct' or 'Incorrect' to indicate which measurements do match this scale factor and which don't.

A model is 1 cm tall.

If the object it was based on was 1.65 m tall, what scale has been used to create the model?

A model pond has been created using a scale 1:100.

It has an area of 0.4 m2.

Is the area of the real pond 40 m2?

Yes

No

• Question 1

A scale of 1:100 means that 1 cm on a model is 100 cm in real life.

When is this statement true?

Sometimes
EDDIE SAYS
This statement may often be true, but it is not always true. The use of the scale 1:100 means that the real life object would be 100 times larger than the scale model, but the units of measurement could change.
• Question 2

A toy car has wheel that are 0.5 cm wide.

How wide are the real wheels if the model has been produced to a scale of 1:48?

Type your answer as a number below without any units, as these have already been provided for you.

EDDIE SAYS
We know that the scale 1:48 means the real life car is 48 times bigger than the model car. So we need to multiply the width of the toy car's wheels by this scale factor to find the width of the real tyres: 0.5 × 48 = 24 cm
• Question 3

A model railway is built to a scale of 1:500.

If the track is 2.3 m long, how long is the track in real life?

Type your answer as a number below without any units, as these have already been provided for you.

EDDIE SAYS
We know that the scale 1:500 means the real life track is 500 times bigger than the model railway. So we need to multiply the length of the model track by this scale factor to find the length of the real track: 2.3 × 500 = 1150 m As there are 1000 metres in a kilometre, we can divide our answer by 1000 to express the length in km: 1150 ÷ 1000 = 1.15 km
• Question 4

A model is made of a garden at a scale of 1:1000.

How tall are the real trees if the model is 1 cm high?

Type your answer as a number below without any units, as these have already been provided for you.

EDDIE SAYS
We know that the scale 1:1000 means the real life garden is 1000 times bigger than the model garden. So we need to multiply the height of the model trees by this scale factor to find the height of the real trees: 1 × 1000 = 1000 m As there are 100 centimetres in a metre, we can divide our answer by 100 to express the height in m: 1000 ÷ 100 = 10 m
• Question 5

Match each pair of scale and real measurements on the left with the correct scale factor (expressed as a ratio) on the right.

## Column B

2 cm model; 10 cm real
1:5
0.3 cm model; 3 cm real
1:10
2 m model; 4 m real
1:2
10 cm model; 1.2 m real
1:12
EDDIE SAYS
Did you remember the process we followed in the Introduction? Let's work through one pair of measurements as an example: 10 cm model; 1.2 m real 1) Make sure the measurements are expressed in the same units: There are 100 cm in 1 m, so 1.2 m = 120 cm 2) Write the two measurements as a ratio: 10:120 3) Cancel the ratio to its simplest form: 10:120 ÷ 10 1:12 Can you use this example to work independently and find the other matches? If you are not feeling totally confident with this process, review the Introduction now before you move on to tackle the rest of this activity.
• Question 6

A toy car is 2 cm long.

If the real car is 1.8 m long, what scale has been used to create the toy?

EDDIE SAYS
Let's follow our process again. 1) Make sure the measurements are expressed in the same units: There are 100 cm in 1 m, so 1.8 m = 180 cm 2) Write the two measurements as a ratio: 2:180 3) Cancel the ratio to its simplest form: 2:180 ÷ 2 1:90 Remember that we read the ratio from left to right, so we must write the model ratio on the left for our answer to be correct.
• Question 7

A 4 cm tall model building has been created using a scale of 1:750 in comparison with the real building.

How tall is the real building in metres?

Type your answer as a number below without any units, as these have already been provided for you.

EDDIE SAYS
We know that the scale 1:750 means the real building is 750 times bigger than the model. So we need to multiply the height of the model building by this scale factor to find the height of the real one: 4 × 750 = 3000 cm We have been asked to express our answer in metres, and we know there are 100 centimetres in a metre. So we can divide our answer by 100 to express the height in m: 3000 ÷ 100 = 30 m
• Question 8

Which of the measurements below have a scale factor of 1:200?

Select either 'Correct' or 'Incorrect' to indicate which measurements do match this scale factor and which don't.

EDDIE SAYS
We can quickly tell if each pair of measurements fit this scale by dividing one of the numbers by the other to see if this creates the target of 200. However, in order to do this, both measurements must be expressed using the same units. Let's work through each, one at a time. 2 ÷ 1 = 2, which does not match 200 so this is an incorrect answer 600 ÷ 3 = 200, which does match so this is a correct answer We need to convert our '10 m' into cm before we start here. There are 100 cm in 1 m, so 10 m = 1000 cm 1000 ÷ 5 = 200, which does match so this is also a correct answer Were you able to locate the two correct answers here?
• Question 9

A model is 1 cm tall.

If the object it was based on was 1.65 m tall, what scale has been used to create the model?

EDDIE SAYS
Let's follow our process again. 1) Make sure the measurements are expressed in the same units: There are 100 cm in 1 m, so 1.65 m = 165 cm 2) Write the two measurements as a ratio: 1:165 3) Cancel the ratio to its simplest form: This cannot be simplified further, as 1 cannot be divided by anything other than itself.
• Question 10

A model pond has been created using a scale 1:100.

It has an area of 0.4 m2.

Is the area of the real pond 40 m2?

No
EDDIE SAYS
This was a really tricky final question, so well done if you got it right! This is really testing how carefully you read and understood the Introduction. Scale factors can only be applied to lengths and other measurements expressed in 2 dimensions. As soon as we move on to working with area or volume, we need to find area or volume scale factors, which are more complex. If you are ready for a challenge, you could try an activity now which focuses on these concepts.
---- OR ----

### What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started