A model of a ship is made to a scale of `1:160`. Find:
the volume of the ship, if the volume of its model is `1.2m^(3)`

Answer

To find the volume of the actual ship given the volume of its model and the scale, we can follow these steps:

### Step 1: Understand the scale
The scale of the model is given as 1:160. This means that 1 unit of measurement on the model corresponds to 160 units of measurement on the actual ship.

### Step 2: Calculate the volume scale factor
Since the volume is a three-dimensional measurement, the scale factor for volume is the cube of the linear scale factor. Therefore, we calculate the volume scale factor as follows:
\[ \text{Volume scale factor} = (160)^3 \]

### Step 3: Calculate \( (160)^3 \)
Now, we calculate \( (160)^3 \):
\[ (160)^3 = 160 \times 160 \times 160 = 4096000 \]

### Step 4: Calculate the volume of the actual ship
To find the volume of the actual ship, we multiply the volume of the model by the volume scale factor:
\[ \text{Volume of the ship} = \text{Volume of the model} \times \text{Volume scale factor} \]
Substituting the values:
\[ \text{Volume of the ship} = 1.2 \, m^3 \times 4096000 \]

### Step 5: Perform the multiplication
Now, we perform the multiplication:
\[ \text{Volume of the ship} = 1.2 \times 4096000 = 4915200 \, m^3 \]

### Final Result
Thus, the volume of the ship is:
\[ \text{Volume of the ship} = 4915200 \, m^3 \]

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