To solve the problem, let's calculate the density of the drink using the given data.

Data provided:

• Density of apple juice: $1.04 \, \text{g/cm}^3$
• Density of fruit syrup: $1.6 \, \text{g/cm}^3$
• Density of sparkling water: $0.99 \, \text{g/cm}^3$
• Volume of apple juice: $35 \, \text{cm}^3$
• Volume of fruit syrup: $25 \, \text{cm}^3$
• Volume of sparkling water: $270 \, \text{cm}^3$

Step 1: Calculate the mass of each component

The mass of a liquid is given by: $\text{Mass} = \text{Density} \times \text{Volume}$

Apple juice:

$\text{Mass of apple juice} = 1.04 \times 35 = 36.4 \, \text{g}$

Fruit syrup:

$\text{Mass of fruit syrup} = 1.6 \times 25 = 40.0 \, \text{g}$

Sparkling water:

$\text{Mass of sparkling water} = 0.99 \times 270 = 267.3 \, \text{g}$

Step 2: Calculate the total mass

The total mass of the drink is the sum of the masses of all components: $\text{Total mass} = 36.4 + 40.0 + 267.3 = 343.7 \, \text{g}$

Step 3: Calculate the density of the drink

The density of the drink is given by: $\text{Density} = \frac{\text{Total mass}}{\text{Total volume}}$

The total volume of the drink is $330 \, \text{cm}^3$ (given). Substituting the values: $\text{Density} = \frac{343.7}{330} \approx 1.042 \, \text{g/cm}^3$

Final Answer:

The density of the drink is: $\boxed{1.042 \, \text{g/cm}^3}$

Do you have any questions or want further clarification?

Here are five related questions for deeper understanding:

1. How would the density change if the volume of fruit syrup was doubled?
2. Can the density of a mixture ever exceed the density of its densest component?
3. What assumptions are made about the volumes in this calculation (e.g., no volume changes due to mixing)?
4. How does temperature affect the densities used in this problem?
5. How can you verify this calculation experimentally?

Tip: Always check the units for consistency when solving density problems!