To solve this question, let’s break it down step-by-step.

1. Identify Given Information:

   • The cola is 9.5% sugar by mass.
   • The density of the cola is 1.03 g/mL.
   • We want to find the volume of cola (in mL) that contains 73.8 grams of sugar.

2. Set up the Equation: Since 9.5% of the cola’s mass is sugar, we can express this as: $\text{Mass of sugar} = 0.095 \times \text{Total mass of cola}$

   Rearranging to solve for the total mass of cola: $\text{Total mass of cola} = \frac{\text{Mass of sugar}}{0.095}$

3. Calculate the Total Mass of Cola: Substituting the given value for the mass of sugar (73.8 grams): $\text{Total mass of cola} = \frac{73.8 \text{ g}}{0.095} = 776.84 \text{ g}$

4. Convert Mass to Volume: Using the density of the cola, which is 1.03 g/mL, we can find the volume $V$ in mL: $V = \frac{\text{Total mass of cola}}{\text{Density}}$ $V = \frac{776.84 \text{ g}}{1.03 \text{ g/mL}} \approx 754.22 \text{ mL}$

So, the volume of cola that contains 73.8 grams of sugar is approximately 754.22 mL.

Would you like a more detailed breakdown of each step or have any questions?

Here are some related questions you might find interesting:

1. How would the volume change if the sugar concentration were increased to 15%?
2. What is the amount of sugar in 500 mL of this cola?
3. How would you calculate the volume if the cola’s density changed to 1.05 g/mL?
4. How much total mass of cola is needed to reach 150 grams of sugar?
5. How would you set up the calculation if the density were given in kg/L instead of g/mL?

Tip: Remember that density links mass and volume, so for questions involving percentages by mass, density is a critical factor to switch between mass and volume calculations.