 # Convert Scale Diagrams to Real Measurements

In this worksheet, students practise converting between scale lengths and real life length. 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 dowsn'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 200cm long in real life.

Example 1: A model car is 1.5 cm tall. If the scale 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 x 100 = 150 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 = 200cm

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

4:200

Out thirs and final step is to simplify this ratio.

1:50

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

Always

Sometimes

Never

A toy car has wheel that are 0.5 cm wide.

How wide are the real wheels if the scale is 1:48

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

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

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

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

1000 cm

10 m

Match the scale with the measurements.

## Column B

2cm scale, 10cm real
1:2
0.3 cm scale: 3 cm real
1:12
2m scale, 4m real
1:5
10cm scale, 1.2 m real
1:10

A toy car is 2cm long. If the real life car is 1.8m long, what is the scale of the model?

## Column B

2cm scale, 10cm real
1:2
0.3 cm scale: 3 cm real
1:12
2m scale, 4m real
1:5
10cm scale, 1.2 m real
1:10

A 4 cm tall model building is at a scale of 1: 750 to the real building it is modelled on.

How tall is the real buiding?

Which of these measurements are correct for the scale 1:200

A model is 1cm tall. If the object it was based on was 1.65m tall, what would the scale be?

A model pond (Scale 1:100) has an area of 0.4m2

Is the area of the real life pond 40m2

Yes

No

• Question 1

A scale of 1:100 means that 1 cm on a model is 100cm 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 toy car has wheel that are 0.5 cm wide.

How wide are the real wheels if the scale is 1:48

24
24cm
24 cm
EDDIE SAYS
We know that 1:48 means the real-life car is 48 times bigger than the model car. If we multiply by 48, we get...
• Question 3

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

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

1150
1150m
1150 m
EDDIE SAYS
Again, we know that the track is 500 times longer in real life so we simply multiply by 500.
• Question 4

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

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

10 m
EDDIE SAYS
Both the answers are the correct length, we just need to read the question carefully. It asks for the height in metres
• Question 5

Match the scale with the measurements.

## Column B

2cm scale, 10cm real
1:5
0.3 cm scale: 3 cm real
1:10
2m scale, 4m real
1:2
10cm scale, 1.2 m real
1:12
EDDIE SAYS
Did you remember the rule? - Make the units the same - Write it as a ratio - Cancel the ratio
• Question 6

A toy car is 2cm long. If the real life car is 1.8m long, what is the scale of the model?

EDDIE SAYS
With these, start by making them the same units and writing them as a ratio. 2:180 Then just cancel it down.
• Question 7

A 4 cm tall model building is at a scale of 1: 750 to the real building it is modelled on.

How tall is the real buiding?

30
30m
30 m
EDDIE SAYS
A scale of 1:750 means the real life building is 4 x 750 = 3000cm tall. We then need to convert it into metres.
• Question 8

Which of these measurements are correct for the scale 1:200

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. 2 ÷ 1 does not give 200
• Question 9

A model is 1cm tall. If the object it was based on was 1.65m tall, what would the scale be?

EDDIE SAYS
A nice and easy one, the 1.65m is 165 cm. Writing these two numbers (with the model one first) would give...
• Question 10

A model pond (Scale 1:100) has an area of 0.4m2

Is the area of the real life pond 40m2

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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