To solve the problem, let's analyze the question:

Problem Statement: A cylindrical container has a capacity of 630 mL. Andi wants to make a coffee mixture using water, espresso, and milk with a ratio of 5:2:3. It is known that the amount of espresso used is 14 mL. The question is asking for the percentage of the coffee mixture that fills the container.

Step-by-Step Solution:

1. Determine the total parts of the mixture: The ratio given is 5:2:3, so the total parts are: $5 + 2 + 3 = 10 \text{ parts}$

2. Determine the volume of one part: Since espresso corresponds to 2 parts and it is given that 14 mL of espresso is used: $\text{Volume of one part} = \frac{14 \text{ mL}}{2} = 7 \text{ mL}$

3. Calculate the total volume of the mixture: Multiply the volume of one part by the total parts: $\text{Total volume} = 7 \text{ mL} \times 10 = 70 \text{ mL}$

4. Calculate the percentage of the mixture relative to the container's capacity: The container has a capacity of 630 mL, so the percentage is: $\text{Percentage} = \frac{70 \text{ mL}}{630 \text{ mL}} \times 100\% \approx 11.11\%$

Answer: The correct answer is closest to E. 11.1%.

Would you like further clarification or additional details? Here are some related questions you might find interesting:

1. How would the percentage change if the amount of espresso was different?
2. What is the effect of altering the ratio on the percentage filling the container?
3. How can you adjust the mixture to exactly fill the container to 100%?
4. What if the total volume exceeded the container’s capacity? How would you solve it?
5. How does changing the ratio to 4:3:3 affect the total volume?

Tip: Always verify your ratio calculations by checking the total parts and ensuring consistency with the given values.