A model of a ship is made to a scale 1 : 300.
The area of the deck of the ship is `180,000 m^2`. Calculate the area of the deck of the model. 

Answer

To solve the problem of finding the area of the deck of the model ship, we will follow these steps:

### Step 1: Understand the Scale Factor
The scale of the model is given as 1:300. This means that 1 unit on the model represents 300 units on the actual ship.

### Step 2: Calculate the Scale Factor for Area
Since we are dealing with area, we need to square the scale factor. The scale factor \( k \) is:
\[ k = \frac{1}{300} \]
Now, we square this scale factor to find the area scale factor:
\[ k^2 = \left(\frac{1}{300}\right)^2 = \frac{1}{90000} \]

### Step 3: Use the Area of the Actual Ship's Deck
The area of the deck of the actual ship is given as \( 180,000 \, m^2 \).

### Step 4: Calculate the Area of the Model's Deck
To find the area of the deck of the model, we multiply the area of the actual ship's deck by the area scale factor:
\[ \text{Area of the model's deck} = k^2 \times \text{Area of the actual ship's deck} \]
Substituting the values we have:
\[ \text{Area of the model's deck} = \frac{1}{90000} \times 180000 \]

### Step 5: Simplify the Calculation
Now, we can simplify this:
\[ \text{Area of the model's deck} = \frac{180000}{90000} = 2 \, m^2 \]

### Final Answer
The area of the deck of the model is \( 2 \, m^2 \).

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