To solve this problem, let's break it down step by step.

1. Total Volume of the Drink: The can contains $300 \, \text{ml}$ of drink.

2. Percentage of Fruit Juice: According to the information, $21\%$ of the drink is fruit juice. To find out how much of the drink is fruit juice, we calculate: $\text{Fruit Juice Volume} = \frac{21}{100} \times 300 \, \text{ml} = 63 \, \text{ml}$

3. Fraction of Fruit Juice that is Apple Juice: Out of this fruit juice, $\frac{1}{10}$ is apple juice. Therefore, the volume of apple juice is: $\text{Apple Juice Volume} = \frac{1}{10} \times 63 \, \text{ml} = 6.3 \, \text{ml}$

So, there are 6.3 milliliters of apple juice in the can.

Would you like more details or have any questions? Here are five related questions to expand on this concept:

1. How would the answer change if the can contained 500 ml instead of 300 ml?
2. What percentage of the total drink is apple juice?
3. If another can had 15% fruit juice, what would be the volume of apple juice in a 300 ml can?
4. How would you express the fraction of apple juice in the drink as a decimal?
5. If the percentage of fruit juice increased to 30%, how much apple juice would be in the can?

Tip: When dealing with percentages, always convert the percentage into a decimal by dividing by 100 before multiplying by the total quantity.