 # Converting Real Measurements to Scale Diagrams

In this worksheet, students practise converting between real life and scale lengths. 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, a toy car doesn't really want to be the same size as a normal car.

When we have this issue, we use a scale diagram or a scale model.

What is a scale diagram?

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.

How are scales written?

Scales are written as a ratio such as 1: 100 or 1:50 000

What does this mean:?

Scales are read left to right. The scale 1:100, for example, would mean that every 1 unit of length on the scale is the same as 100 units in real life.

So something that was 2 cm long in real life would be 200 cm long in real life.

Example 1: A model car is 3m tall. If the scale is 1:100, how tall would the model car be?

We know that there is a factor of 100 and that the model is smaller

All we need to do here is change the units into cm and divide by the scale factor.

300 ÷ 100 = 3 cm

Example 2: A model is made of a 2 m tall man. If the model is 4 cm tall, what is the scale?

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

2m = 200 cm

Step 2 is to write these numbers as a ratio (remember the model comes first))

4:200

Out third and final step is to simplify this ratio.

1:50

A scale of 1:100 means that 2 m on a model is 2 cm in real life

Always

Sometimes

Never

A car is 1.8 m wide. If it is made into a 1:48 scale model, how wide is the model in cm?

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

If the real track is 2.8 km long, how many metres will the model track be?

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

How tall in cm would the model tree be if the real one were 1.2 m tall?

1200 cm

0.12 cm

Match the scale with the measurements.

## Column B

5cm real , 1cm model
1:10
14cm real, 1.4cm model
1:5
15m real, 7.5 m model
1:12
4.8 cm real, 0.4cm model
1:2

A lorry is 7m long. If I make a model that is 3.5 cm long, what is the scale?

## Column B

5cm real , 1cm model
1:10
14cm real, 1.4cm model
1:5
15m real, 7.5 m model
1:12
4.8 cm real, 0.4cm model
1:2

The Burj Khalifa in Dubai is 828 metres tall. If I made a 1: 50 scale model, how tall would it be?

Which of these measurements are correct for the scale 1:150

A woman is 1.32m tall. If I made a 2 cm tall model, what would the scale be?

A building has a surface area of 1600 m2.

Would a scale model (1:1000) have a surface area of 1.6m2?

Yes

No

• Question 1

A scale of 1:100 means that 2 m on a model is 2 cm in real life

Sometimes
EDDIE SAYS
This is true, but not always. What it means is that the real-life model is 100 times bigger.
• Question 2

A car is 1.8 m wide. If it is made into a 1:48 scale model, how wide is the model in cm?

375
3.75 cm
3.75
EDDIE SAYS
We know that 1:48 means the real-life car is 48 times bigger than the model car. If we divide by 48, we get...
• Question 3

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

If the real track is 2.8 km long, how many metres will the model track be?

5.6m
5.6 m
5.6
EDDIE SAYS
Again, we know that the track is 500 times longer in real life so we simply divide by 500.
• Question 4

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

How tall in cm would the model tree be if the real one were 1.2 m tall?

0.12 cm
EDDIE SAYS
We are making a smaller model here, so we need to divide by 1000
• Question 5

Match the scale with the measurements.

## Column B

5cm real , 1cm model
1:5
14cm real, 1.4cm model
1:10
15m real, 7.5 m model
1:2
4.8 cm real, 0.4cm model
1:12
EDDIE SAYS
Did you remember the rule? - Make the units the same - Write it as a ratio (with the scale size first) - Cancel the ratio
• Question 6

A lorry is 7m long. If I make a model that is 3.5 cm long, what is the scale?

EDDIE SAYS
With these, start by making them the same units and writing them as a ratio. 3.5: 700 Then just cancel it down.
• Question 7

The Burj Khalifa in Dubai is 828 metres tall. If I made a 1: 50 scale model, how tall would it be?

16.56
16.56m
16.56 m
EDDIE SAYS
A scale of 1:50 means the scale model building is 828 ÷ 50
• Question 8

Which of these measurements are correct for the scale 1:150

EDDIE SAYS
We can quickly tell if it fits the scale by dividing one of the numbers by the other when they have the same units. 15 ÷ 1 does not give 150
• Question 9

A woman is 1.32m tall. If I made a 2 cm tall model, what would the scale be?

EDDIE SAYS
How did you do? Did you get that 1.32 m is 132 cm? Writing these two numbers (with the model one first) and cancelling down would give...
• Question 10

A building has a surface area of 1600 m2.

Would a scale model (1:1000) have a surface area of 1.6m2?

No
EDDIE SAYS
This one is testing how closely you read the intro. Scale factors like this are only given for lengths, not areas.
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