### Scale drawing

Linear Scale |
---|

Making Scale Drawing |

Assessment questions |

Given a scale diagram we can make drawing measurements.

Similarly, real (actual) measurements can be made on a real object.

Linear scale shows, the relationship between drawing (scale) length and actual length.

Linear scale of a diagram is given in statement or ratio form.

When the ratio form is used the unit of measurement for the drawing length and actual length is the same.

It is not always possible to draw on paper the actual size of real-life objects

such as the real size of a car, an airplane, house

we need scale drawings to represent the size like the one you have seen.

#### Example 1

In a scale diagram 1cm represents 50 m

(a) Write the scale in ratio form.

(b) Find the drawing length for 1.25 km.

(c) Find the actual length in kilometers corresponding to a length of 10.5cm on the diagram.

#### Example 2

In a diagram of a plan of a factory a length of 2.5 cm represents an actual length of 12.5 m

(a) Work out the linear scale in ratio form.

(b) Find the distance on the plan between two buildings which are 35 m apart.

## Conversions to recall

- 1 km =1000 m
- 1 km = 100,000 cm
- 1 m = 100 cm
- 1 ha = 10,000 m
^{2}

## Scale in statement form

1cm represents 3m can be written as:

1cm represents 300cm.

It can also be written **as a ratio **

1:300

Read as; *one to three hundred.*

For every unit of drawing there are three hundred similar units of real length.

**Drawing length: real length**

#### Write each of the following scales as a ratio

(ii)1cm represents 5m

(iii)1cm represents 200m

#### Complete the following statements

(ii)The scale 1:4000000 can be written as 1cm represents ____km.

#### Solution

(i)1:400000 (ii)1:500 (iii)1:20000 (iv)100m (v)40km

### Why are scale drawings important?

Careers that involve construction, architecture, city planning, design and map-reading all require knowledge of scale drawings

You also need to able to use scale-drawings when you are travelling (maps).

#### Example

use the map of Maine to estimate the distance of China and New Sweden.

- liner-scale_img1 by elimu used under CC_BY-SA
- 93bc2d6c-012a-4fc7-a5a0-0bb031654c97 by elimu used under CC_BY-SA
- liner-scale_img3 by elimu used under CC_BY-SA
- liner-scale_img3 by elimu used under CC_BY-SA
- liner-scale_img4 by elimu used under CC_BY-SA
- liner-scale_img4 by elimu used under CC_BY-SA
- liner-scale_img5 by elimu used under CC_BY-SA
- SCALE_11 by Unknown used under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License

All work unless implicitly stated is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.