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To solve this problem, we need to calculate how many glasses Aaron can fill with one gallon of fruit juice.

### Given Information:
- Total volume of fruit juice = 1 gallon = 231 cubic inches.
- Each glass is a cylinder with:
  - Diameter \( d = 2.7 \) inches,
  - Height \( h = 8 \) inches.

### Step-by-step Solution:

1. **Volume of a cylindrical glass:**
   The volume \( V \) of a cylinder is given by the formula:
   \[
   V = \pi r^2 h
   \]
   where \( r \) is the radius and \( h \) is the height.

   The radius \( r \) is half the diameter:
   \[
   r = \frac{2.7}{2} = 1.35 \, \text{inches}
   \]
   
   Therefore, the volume of one glass is:
   \[
   V = \pi (1.35)^2 (8)
   \]
   Let's calculate this.

2. **Finding the maximum number of glasses \( n \):**
   To find \( n \), we need to divide the total volume of juice (231 cubic inches) by the volume of one glass:
   \[
   n = \frac{231}{V}
   \]

Let me calculate this for you.The maximum number of cylindrical glasses that Aaron can fill with one gallon of juice is approximately 5. Since we can't have a fraction of a glass, the maximum whole number value of \( n \) is 5 glasses.

Would you like more details on any part of the solution or further clarifications?

Here are 5 related questions you might explore:
1. How would the result change if the glasses were taller or shorter?
2. What if the diameter of the glasses increased to 3 inches?
3. How can we calculate the volume of a cylindrical container without knowing the height?
4. What is the impact of using metric units (liters) instead of cubic inches?
5. Can we calculate the surface area of the glass based on the same dimensions?

**Tip:** When dealing with cylinders, remember that both the radius and height directly affect the volume, so even small changes in these dimensions can significantly impact the result!

Aaron just bought a premium fruit juice and wanted to pour one gallon (231 cubic inches) of it into n identical glasses. If each cylindrical glass has a diameter of 2.7 inches and a height of 8 inches, what is the maximum value of n?

Learn how to calculate the maximum number of glasses that can be filled with one gallon of fruit juice using cylindrical volume calculations. This problem involves calculating the volume of a cylinder and applying it to real-world scenarios. Suitable for Grades 8-10.

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