Let's work through the problem step by step.

Given Data:

• The density of apple juice is $1.04 \, \text{g/cm}^3$.

• The density of fruit syrup is $1.6 \, \text{g/cm}^3$.

• The density of sparkling water is $0.99 \, \text{g/cm}^3$.

• Volume of apple juice: $35 \, \text{cm}^3$

• Volume of fruit syrup: $25 \, \text{cm}^3$

• Volume of sparkling water: $270 \, \text{cm}^3$

Total volume of the mixture: $330 \, \text{cm}^3$

Step 1: Calculate the mass of each component

1. Mass of apple juice: $\text{Mass of apple juice} = \text{Density} \times \text{Volume} = 1.04 \times 35 = 36.4 \, \text{g}$

2. Mass of fruit syrup: $\text{Mass of fruit syrup} = \text{Density} \times \text{Volume} = 1.6 \times 25 = 40 \, \text{g}$

3. Mass of sparkling water: $\text{Mass of sparkling water} = \text{Density} \times \text{Volume} = 0.99 \times 270 = 267.3 \, \text{g}$

Step 2: Calculate the total mass of the drink

$\text{Total mass} = 36.4 + 40 + 267.3 = 343.7 \, \text{g}$

Step 3: Calculate the density of the drink

The density of the drink is given by: $\text{Density of the drink} = \frac{\text{Total mass}}{\text{Total volume}} = \frac{343.7}{330} \approx 1.041 \, \text{g/cm}^3$

So, the density of the drink is 1.041 g/cm³, correct to three decimal places.

Would you like further details or have any questions?

Relative questions:

1. How does the density of a mixture relate to the individual densities of its components?
2. Why is it important to know the density of a drink in real-world scenarios?
3. What would happen to the density if we increased the amount of fruit syrup?
4. Can the density of a mixture ever be lower than the lowest density component?
5. How would you calculate the mass if the density and volume are given but in different units?

Tip:

Always ensure the units are consistent (such as g/cm³) when calculating densities or any related quantities!