Ratio, Proportion and Percentages • Topic 3 of 3

Scale Drawings and Applications

What is a Scale Drawing?

A scale drawing is a drawing that represents a real object with all lengths reduced or enlarged proportionally. The scale is the ratio of the length in the drawing to the actual length.

Scale Notation:

  • \(1 : 50\) means 1 unit in the drawing represents 50 units in real life
  • \(1 \text{ cm} : 5 \text{ m}\) means 1 cm in drawing = 5 m in reality (units differ)

Types of Scales:

TypeExampleMeaning
Reduction scale\(1 : 100\)Drawing is smaller than real object (maps, floor plans)
Enlargement scale\(5 : 1\)Drawing is larger than real object (microscope images)

Using Scale Drawings:

  • Actual length = Drawing length × Scale factor
  • Drawing length = Actual length ÷ Scale factor

Real-Life Applications:

  • Maps: 1 cm = 1 km, etc.
  • Architectural blueprints: 1 cm = 1 m
  • Model making: Model cars, airplanes
  • Engineering drawings: Machine parts

Scale Factor:

The number used to multiply the drawing dimensions to get actual dimensions.

Scale Drawings and MapsMap (Scale 1:50,000)SchoolParkMarket2.4 cm on map= 2.4 × 50,000 cm= 1.2 km actualScale FormulaScale = Map length ÷ Actual lengthActual = Map length ÷ Scalee.g. Map: 3cm, Scale 1:25000Actual = 3 × 25000 cm = 750 m = 0.75 km
Solved Examples
1
Worked Example

A map has a scale of \(1 : 50,000\). What actual distance does 8 cm on the map represent?

Solution
  • Scale means 1 cm on map = 50,000 cm in reality
  • 8 cm on map = \(8 \times 50,000 = 400,000\) cm
  • Convert to km: \(400,000 \div 100,000 = 4\) km

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Answer: 4 km **Example 2:** In a scale drawing, a wall is 12 cm long. The scale is $1 : 50$. What is the actual length of the wall in meters? *Solution:* - Actual length = Drawing length × Scale factor - $12 \times 50 = 600$ cm - Convert to meters: $600 \div 100 = 6$ m - **Answer:** 6 m **Example 3:** The actual length of a car is 4.8 m. In a scale drawing, it is 8 cm long. Find the scale ratio. *Solution:* - Convert actual length to same unit as drawing: $4.8 \text{ m} = 480 \text{ cm}$ - Scale ratio = Drawing length : Actual length = $8 : 480$ - Simplify: Divide both by 8 → $1 : 60$ - **Answer:** $1 : 60$

Key Points

  • A scale drawing represents a real object with proportional lengths
  • Scale = drawing length : actual length
  • For reduction: scale factor < 1 (e.g., 1:100)
  • For enlargement: scale factor > 1 (e.g., 50:1)
  • Always convert to same units before working with scales
  • Use proportion to find actual or drawing lengths: \(\frac{\text{drawing}}{\text{actual}} = \text{scale}\)
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.A scale shows how a drawing length relates to the:
Explanation: Actual length.
Q2.A scale of $1:100$ means $1$ cm represents:
Explanation: $100$ cm.
Q3.Scale drawings keep the same:
Explanation: Shape (similar figures).
Q4.On a $1:100$ map, $3$ cm represents:
Explanation: $300$ cm $=3$ m.
Practice more MCQs → 📝 Assignment · 35 marks