A model of a ship is made to a scale 1 : 300.
The volume of the model is `6.5 m^3`. Calculate the volume of the ship.

Answer

To solve the problem, we need to find the volume of the actual ship based on the given scale of the model. The scale is given as 1:300, meaning that every dimension of the model is 1/300 of the corresponding dimension of the actual ship.

### Step-by-Step Solution:

1. **Understand the Scale Factor**:
The scale of the model is 1:300. This means that for every 1 unit of measurement on the model, the actual ship measures 300 units. Therefore, the scale factor \( k \) is:
\[ k = \frac{1}{300} \]

2. **Volume Relationship**:
The volume of similar objects is related by the cube of the scale factor. If \( V_{model} \) is the volume of the model and \( V_{ship} \) is the volume of the actual ship, then:
\[ V_{model} = k^3 \times V_{ship} \]

3. **Substituting Known Values**:
We know the volume of the model:
\[ V_{model} = 6.5 \, m^3 \]
Now, substituting the scale factor into the volume relationship:
\[ 6.5 = \left(\frac{1}{300}\right)^3 \times V_{ship} \]

4. **Calculate \( k^3 \)**:
First, calculate \( k^3 \):
\[ k^3 = \left(\frac{1}{300}\right)^3 = \frac{1}{300^3} = \frac{1}{27000000} \]

5. **Setting Up the Equation**:
Now, substitute \( k^3 \) back into the equation:
\[ 6.5 = \frac{1}{27000000} \times V_{ship} \]

6. **Solving for \( V_{ship} \)**:
To find \( V_{ship} \), multiply both sides by \( 27000000 \):
\[ V_{ship} = 6.5 \times 27000000 \]

7. **Performing the Multiplication**:
Now, calculate the volume of the ship:
\[ V_{ship} = 6.5 \times 27000000 = 175500000 \, m^3 \]

### Final Answer:
The volume of the ship is \( 175500000 \, m^3 \).

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