Meaning of Scale Drawing:

A scale drawing is a drawing that shows an object or place in proportion to its actual size but reduced or enlarged using a scale. It helps us to represent large distances (like maps, buildings, or roads) or very small objects (like machine parts) on paper in a convenient size.

A scale is the ratio of the drawing’s size to the actual size of the object. In a scale drawing, all parts are drawn to the same scale so that the drawing remains accurate.

1. Full Scale: When the drawing is made the same size as the real object.
   Example: Scale 1 : 1 (no reduction or enlargement).


2. Reducing Scale: When the drawing is smaller than the real object.
   Example: Scale 1 : 50 means 1 unit on drawing = 50 units in real life.


3. Enlarging Scale: When the drawing is larger than the real object.
   Example: Scale 2 : 1 means 2 units on drawing = 1 unit in real life.

1. It helps us to represent large objects like buildings or roads on small paper.


2. It helps us to represent small objects like machine parts in a larger form.


3. It is useful in construction, geography, engineering, and architecture.


4. It helps us to calculate distances and dimensions accurately.

1. 1 : 10 – for small machine parts.


2. 1 : 50 or 1 : 100 – for building plans.


3. 1 : 500 or 1 : 1000 – for site plans.


4. 1 : 50,000 – for geographical maps.

If a scale is 1 : 50, it means 1 cm on drawing = 50 cm in real life.

If a scale is 1 : 1000, it means 1 cm on drawing = 1000 cm = 10 m in real life.

If a scale is 2 : 1, it means 2 cm on drawing = 1 cm in real life (enlarged).

Examples

Example 1: Reducing Scale (Map Problem)

A map is drawn to a scale of 1 : 50,000. Find the actual distance between two towns that are 4 cm apart on the map.

Solution:

Scale 1 : 50,000 means 1 cm = 50,000 cm.

Step 1: Actual distance = 4 × 50,000 = 200,000 cm.
Step 2: Convert to kilometres → 200,000 ÷ 100,000 = 2 km.

Answer: Actual distance = 2 km

Text diagram:

Town A ●––––––––––● Town B
         4 cm on map  →  2 km in real life

Example 2: Finding Distance on Drawing

A football field is 100 m long. If it is drawn to a scale of 1 : 500, find the length of the field on paper.

Solution:

1 cm = 500 cm. Convert 100 m to cm → 10,000 cm.

Drawing length = 10,000 ÷ 500 = 20 cm.

Answer: 20 cm on paper.

Example 3: Enlarging Scale

A watch gear has a real diameter of 2 cm. It is drawn to a scale of 5 : 1. Find the diameter of the drawing.

Solution:

Scale 5 : 1 → 5 cm on drawing = 1 cm real.

Drawing diameter = 5 × 2 = 10 cm.

Answer: Drawing diameter = 10 cm

Example 4: Using Scale to Find Actual Length

A road on a map measures 8 cm, and the scale of the map is 1 : 25,000. Find the actual distance in kilometres.

Solution:

1 cm = 25,000 cm
8 cm = 8 × 25,000 = 200,000 cm
Convert to metres → 200,000 ÷ 100 = 2,000 m
Convert to km → 2,000 ÷ 1,000 = 2 km

Answer: The road is 2 km long.

Example 5: Finding Scale Used

A drawing of a wall 12 m long is 24 cm on paper. Find the scale of the drawing.

Solution:

Convert 12 m to cm → 1,200 cm.
Scale = drawing length : actual length = 24 : 1,200 = 1 : 50.

Answer: Scale = 1 : 50

Example 6: Real-life Plan (House Room)

A room measures 5 m by 3 m. Drawn to a scale of 1 : 100, find the dimensions on paper.

Solution:

1 cm represents 1 m.

Length = 5 m → 5 cm
Width = 3 m → 3 cm

Text diagram:

5 cm
┌──────────────┐
│              │ 3 cm
└──────────────┘

Constructing Scale Drawings (Steps)

1. Choose a suitable scale to fit the paper.


2. Measure the actual dimensions of the object.


3. Convert actual measurements to scale measurements.


4. Draw neatly using a ruler.


5. Label and indicate the scale used.

Quantitative Reasoning Example

A school compound is rectangular. Its actual length is 120 m and width is 80 m. It is drawn to a scale of 1 : 400. Find:

1. The dimensions on the drawing.


2. The area of the compound on the drawing.


3. The actual area of the compound.

Solution:

Length on drawing = 120 ÷ 4 = 30 cm
Width on drawing = 80 ÷ 4 = 20 cm

Area on drawing = 30 × 20 = 600 cm²
Actual area = (Scale factor)² × Drawing area = 400² × 600 = 96,000,000 cm² = 9,600 m²

Text diagram:

30 cm
┌──────────────────────────┐
│                          │ 20 cm
│     SCHOOL COMPOUND      │
└──────────────────────────┘

Summary Table

Scale Type	Meaning	Example	Used For
Full Scale	Actual size	1 : 1	Machine part drawings
Reducing Scale	Smaller drawing	1 : 100	Maps, buildings
Enlarging Scale	Larger drawing	2 : 1	Small parts

Key Formulas

1. Scale = Drawing length ÷ Actual length


2. Actual length = Drawing length ÷ Scale ratio


3. Drawing length = Actual length × Scale ratio


4. Area (drawing) × (Scale ratio)² = Actual area