A model of an aeroplane is made to a scale of 1 : 400. Calculate :
  the length, in cm, of the model, if the length of the aeroplane is 40 m. 

Answer

To solve the problem of finding the length of the model of an aeroplane made to a scale of 1:400, given that the actual length of the aeroplane is 40 meters, we can follow these steps:

### Step 1: Understand the Scale
The scale of 1:400 means that 1 unit of measurement on the model is equal to 400 units of the same measurement on the actual aeroplane.

### Step 2: Convert the Length of the Aeroplane to Centimeters
Since the length of the aeroplane is given in meters, we need to convert it to centimeters for consistency with the model's scale.
- 1 meter = 100 centimeters
- Therefore, 40 meters = 40 × 100 = 4000 centimeters.

### Step 3: Set Up the Scale Equation
Using the scale, we can set up the following equation:
\[ \frac{\text{Model Length}}{\text{Aeroplane Length}} = \frac{1}{400} \]
Let the model length be \( x \). The aeroplane length is 4000 cm (from Step 2).

### Step 4: Substitute the Known Values
Substituting the known values into the equation gives:
\[ \frac{x}{4000} = \frac{1}{400} \]

### Step 5: Cross-Multiply to Solve for \( x \)
Cross-multiplying gives:
\[ x \cdot 400 = 4000 \cdot 1 \]
This simplifies to:
\[ 400x = 4000 \]

### Step 6: Divide to Find the Model Length
Now, divide both sides by 400 to solve for \( x \):
\[ x = \frac{4000}{400} = 10 \]

### Conclusion
The length of the model of the aeroplane is **10 centimeters**.

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