Scale drawings - Year 7 PDF Download

Key points

• Scale Drawings:
• Scale drawings are accurate representations of real objects where lengths are adjusted by a scale factor.
• The ratio of corresponding edge lengths in the drawing to real life is maintained.
• These drawings are often smaller depictions of larger objects like buildings, gardens, or vehicles.
• They can also be larger representations of small objects such as watch parts or medical instruments.
• Scales in drawings are expressed as ratios, comparing lengths on the diagram to real lengths.
• All dimensions in a scale drawing are reduced proportionally, usually in centimeters and millimeters.
• For instance, 1 cm on a scale drawing might represent 1 meter in real life, indicating a scale of 1:100.
• Understanding unit conversion, simplifying ratios, and solving proportion problems are essential in using scales effectively.

Scale Factor and Scale Drawing

Scale Factor: The scale factor is the ratio of corresponding edge lengths in a drawing to real life. It helps us understand how the size of objects in a drawing compares to their actual size.

• Scale Drawing: A scale drawing is a precise representation of an object where all lengths in the drawing are proportionate to the actual object. These drawings can represent objects both larger and smaller than reality. For instance, buildings, gardens, vehicles, as well as intricate parts like those in watches or medical instruments can be accurately depicted through scale drawings.

Scales in Ratio: Scales are expressed as ratios, which involve comparing lengths on a diagram to their actual lengths. In a scale drawing, all dimensions are uniformly reduced, often measured in centimeters and millimeters. For example, 1 centimeter on a scale drawing that represents 1 meter in real life indicates a scale of 1:100.

Ratio and Unitary Ratio

A ratio is a part-to-part comparison. When using scales, understanding unit conversion, simplifying ratios, and solving proportion problems are essential skills.

• When writing and using scales, understanding conversion between units, simplifying ratios, and solving ratio and proportion problems can help.
• A unitary ratio appears in the form 1 : n or n : 1, indicating a specific relationship between units.

Unitary Ratio Explained

A unitary ratio in the form 1 : n or n : 1 signifies a direct comparison between one unit on a scale drawing and a certain number of units in real life.

• 1 : n indicates that one unit on the scale drawing represents n units in real life. For instance, a scale of 1 : 500 means 1 cm on the drawing represents 500 cm in reality.
• n : 1 indicates that n units on the scale drawing represent one unit in real life. For example, a scale of 200 : 1 implies that 200 mm on the drawing represents 1 mm in reality.

Understanding Scale Ratios

• 1 : n - In this scenario, the scale indicates that n units on a scale drawing represent one unit in real life. For instance, a scale of 200:1 implies that 200 mm on the scale drawing corresponds to 1 mm in reality.
• n : 1 - This ratio signifies that n units on a scale drawing represent one unit in real life.

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How to Express a Scale as a Ratio

To represent a scale as a ratio, follow these steps:

• Begin by noting down the length on the scale drawing followed by the corresponding length on the actual object.
• Ensure both lengths are in the same smaller units for comparison.
• Write down the ratio without including any units.
• If any values are in decimals, multiply them by a power of ten to convert them into integers.
• Simplify the ratio by dividing both values by their highest common factor (HCF) to obtain a simplified form.

Definition of Highest Common Factor (HCF)

The highest common factor (HCF) is the largest factor that divides into the selected numbers.

For example, 10 is the highest common factor of 30 and 20. It is denoted as HCF.

Examples

Here is an example illustrating the concept:

• When a scale drawing of 4 centimetres represents 5 metres on the real object, we can determine the scale used. To find the scale in its simplest form, we need to calculate the ratio of these two lengths.

Understanding Scale Drawings

Key Concepts

• Understanding ratios and scale drawings
• Converting lengths between different units
• Simplifying ratios using the highest common factor (HCF)
• Determining scales based on given measurements

Ratio and Proportion

Question

• Example 1: Four centimetres represents five metres.
• The scale drawing length of 4 centimetres represents the corresponding length of 5 metres on the real object.
• Work out the scale that has been used and write it in its simplest form.

Paraphrased Explanation

• Ratio Simplification: When simplifying ratios, divide both values by their highest common factor (HCF) to obtain an equivalent ratio.
• Decimal Conversion: To convert a ratio with decimals into integers, multiply both parts by 10 or a suitable power of 10.
• Scale Drawing: In scale drawings, a certain length on the drawing represents a specific length on the actual object in a proportional manner.
• Simplified Ratios: Simplified ratios provide a clearer view of the relationship between the quantities involved.

Using a scale to determine measurements for a scale drawing

• For a scale diagram smaller than the real object:
• Express the scale as a unitary ratio in the form 1 : n.
• Convert each real length to centimeters.
• Divide each real length by the scale (n).
• For a scale diagram larger than the real object:
• Express the scale as a unitary ratio in the form n : 1.
• Multiply each real length by the scale (n).
• Convert each real length to centimeters, if necessary.

Examples

• Image caption: Use a scale of 1 : 20 to find the measurements for a scale drawing of a bedroom. The floorplan of the bedroom measures 3.4 meters by 2.7 meters.
• Image caption: The scale 1 : 20 implies that one centimeter on the scale drawing represents 20 cm in real life. Multiplying the drawn length by 20 gives the real length. Dividing the real length by 20 gives the drawn length. To find the scale drawing measurements in this instance, the real lengths are divided by 20.

Understanding Scale Drawings

• Scale Ratios in Scale Drawings

  When creating scale drawings, a scale ratio like 1 : 20 is used. This means that each real length is divided by 20 to get the scaled length. For instance, if a real length is 3.9 metres, it converts to 390 cm, and 2.7 metres converts to 270 cm.

  

• Calculating Measurements in Scale Drawings

  To find the measurements on a scale drawing, divide each real measurement by the scale ratio. For example, if the real length is 340 units, and the scale is 1 : 20, the length on the scale drawing will be 17 units. Similarly, for a width of 270 units, the width on the drawing will be 13.5 units.

  

• Using Different Scale Ratios

  When dealing with different scale ratios like 15 : 2, apply the ratio to find measurements for scale drawings. For instance, with a real length of 8 mm and a real width of 3 mm, you can use the 15 : 2 scale to determine the corresponding lengths on the drawing.

  

• Expressing Ratios as Unitary Ratios

  To simplify scale ratios into unitary ratios, divide both parts of the ratio. For a ratio like 15 : 2, dividing by 2 yields 7.5 : 1. This unitary ratio helps in easier understanding and application in scale drawings.

  

Understanding Scale Drawing Concepts

• Image Caption: The concept of a scale 7√5 : 1 represents a unitary ratio as n : 1. In this scale, 7√5 cm on the drawing corresponds to 1 cm in real life. To find the real length from the drawing, divide the drawn length by 7√5. Conversely, to find the drawn length from the real length, multiply the real length by 7√5. The scale drawing magnifies the size of the machine component by a scale factor of 7√5.

• Image Caption: When determining measurements in a scale drawing, each real length is multiplied by the scale factor (7√5). For example, if the real length is 8, multiplying by 7√5 gives a component length of 60 mm. Similarly, if the real width is 3, multiplying by 7√5 results in a component width of 22√5 mm.

Example Scenario: Scale 1 to 20

• Slide 1 of 8: Real length is 3.4 meters and real width is 2.7 meters. Using a scale of 1 : 20, determine the measurements for a scale drawing of a bedroom with a floorplan measuring 3.4 meters by 2.7 meters.

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Using a Scale to Find Real Lengths

To determine the actual lengths from a scale diagram, considering whether the object is larger or smaller:

• Express the scale as a unitary ratio in the form 1 : n.
• Multiply each scaled length by the scale factor (n).
• If necessary, convert the units accordingly.

• Represent the scale as a unitary ratio in the form n : 1.
• Divide each scaled length by the scale factor (n).
• If needed, convert the units appropriately.

Examples

• Given a scale drawing with a ratio of 2 : 25, where the distance between wall sockets is 25⅙ centimeters, determine the actual distance in meters.


For the given example, the scale ratio is reduced to 1 : 12⅚ by dividing both parts by 2 (2 ÷ 2 = 1 and 25 ÷ 2 = 12⅚).

Understanding Scale Drawing

• Definition of Scale Drawing: A scale drawing is a representation of an object or space that is drawn to a smaller or larger scale compared to the actual object.
• Scale Ratio Explanation: The scale ratio, such as 1 : 12⅘, indicates the relationship between the measurements on the drawing and in real life. For example, 1 cm on the scale drawing represents 12⅘ cm in reality.
• Calculating Real Length: To find the real length from a scale drawing, you multiply the drawn length by the scale factor. For instance, if the scale factor is 12⅘, the real length is obtained by multiplying the drawn length by 12⅘.

Examples of Scale Drawing Applications

Example 1: Enlarging Machine Components

• Scenario: A scale drawing enlarges a machine component by a scale factor of 12⅘.
• Calculation: If the scaled length is 25⅙ cm, multiplying it by the scale (12⅘) gives the real distance, which is 320 cm or 3⅞ meters.

Example 2: 3D Printer Component Width

• Scenario: A 3D printer creates small components using a scale drawing with a ratio of 50 : 1, where the width of one component is 2 cm.
• Finding Actual Width: To determine the actual width, you must consider the scale ratio and the measurements provided in the scale drawing.

Importance of Scale Drawing

• Visualization: Scale drawings help in visualizing objects or structures accurately before they are built or constructed.
• Precision: They aid in maintaining precision and proportionality in design and engineering endeavors.

Understanding Scale Drawings

A scale drawing is a representation of an object or space that is proportionally smaller or larger than the actual object or space. It helps us visualize and understand the real dimensions of objects.

Key Concepts:

• Scale Ratio Explanation
• When we talk about a scale ratio like 50 : 1, it signifies a unitary ratio where n : 1 represents the ratio. For example, in a 50 : 1 scale, 50 cm on the scale drawing represents 1 cm in real life.
• To find the real length from a scale drawing, you divide the drawn length by the scale factor. In this case, the scale drawing is 50 times larger than the actual component.
• Calculating Real Length from Scale Drawing
• For instance, if we have a scaled length of 2 cm and the scale is 50, you can determine the real length by dividing 2 by 50, resulting in 0.04 cm. This is equivalent to 0.4 millimeters.

Examples:

Question

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Practise using scale drawings

Quiz

Practise using scale drawings in this quiz. You may need a pen and paper to complete these questions.

Real-world maths

Scale drawings are used by designers to plan and adjust details before actual production so that all problems can be addressed.

CAD (computer-aided design) relies heavily on scaling software, interpreted by automotive, structural and civil engineers. A scale drawing of a car has the same shape as the real car that it represents but a different size.

People searching for a house to buy can access floorplans of properties and see a scale drawing that enables them to get a feel for the layout of the house. They may plan what furniture to buy that will fit in each room.

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Summary and Explanation

• Designers use scale drawings to plan and adjust details before production to address potential problems.
• CAD heavily relies on scaling software, used by automotive, structural, and civil engineers for design.
• A scale drawing represents the same shape as the real object but in a different size, as seen in car designs.
• Prospective house buyers can access property floorplans with scale drawings to understand the layout and plan furniture placement.