A model aeroplane has a scale of $$ 1: 40 $$. (a) If the wing span on the model is 25 centimetres, what would be the wingspan of the real aeroplane? (b) If the real aeroplane has length 8 metres, what is the length of the model aeroplane?

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UpStudy AI · Accepted Answer

To solve the problems involving the scale model of the aeroplane, we use the concept of scale ratios. A scale of $$1:40$$ means that **1 unit on the model corresponds to 40 units on the real aeroplane**.

### Part (a)
**Given:**  
- **Model wingspan:** 25 centimeters

**To find:**  
- **Real aeroplane wingspan**

**Calculation:**  
$$
\text{Real Wingspan} = \text{Model Wingspan} \times \text{Scale Factor} = 25\, \text{cm} \times 40 = 1000\, \text{cm}
$$
$$
1000\, \text{cm} = 10\, \text{meters}
$$

**Answer:**  
The real aeroplane has a wingspan of **10 meters**.

---

### Part (b)
**Given:**  
- **Real aeroplane length:** 8 meters

**To find:**  
- **Model aeroplane length**

**Calculation:**  
$$
\text{Model Length} = \frac{\text{Real Length}}{\text{Scale Factor}} = \frac{8\, \text{meters}}{40} = 0.2\, \text{meters}
$$
$$
0.2\, \text{meters} = 20\, \text{centimeters}
$$

**Answer:**  
The model aeroplane has a length of **20 centimeters**.

---

**Summary:**
- **(a)** 10 meters
- **(b)** 20 centimeters
- **(a)** The real aeroplane's wingspan is 10 meters. - **(b)** The model aeroplane's length is 20 centimeters.

A model aeroplane has a scale of .
(a) If the wing span on the model is 25 centimetres,
what would be the wingspan of the real aeroplane?
(b) If the real aeroplane has length 8 metres,
what is the length of the model aeroplane?

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A model aeroplane has a scale of . (a) If the wing span on the model is 25 centimetres, what would be the wingspan of the real aeroplane? (b) If the real aeroplane has length 8 metres, what is the length of the model aeroplane?