Jim has identical drinking glasses each in the shape of a right circular cylinder with internal diameter of 3 inches. He pours milk from a gallon jug into each glass until it is full. If the height of milk in each glass is about 6 inches, what is the largest number of full milk glasses that he can pour from one gallon of milk? (Note: There are 231 cubic inches in 1 gallon.)

Options

A. 2
B. 4
C. 5
D. 6

Explanation

To solve the problem, we need to determine how many full glasses of milk Jim can pour from one gallon of milk, given the dimensions of the glasses.

### Step-by-Step Solution:

1. **Identify the dimensions of the glass:**
- The internal diameter of the glass is given as 3 inches.
- The radius (r) can be calculated as:
\[ r = \frac{\text{diameter}}{2} = \frac{3}{2} = 1.5 \text{ inches} \]

**Hint:** Remember that the radius is half of the diameter.

2. **Identify the height of the milk in the glass:**
- The height (h) of the milk in each glass is given as 6 inches.

**Hint:** The height is provided directly in the problem.

3. **Calculate the volume of one glass:**
- The formula for the volume (V) of a right circular cylinder is:
\[ V = \pi r^2 h \]
- Substitute the values of r and h into the formula:
\[ V = \pi (1.5)^2 (6) \]
- Calculate \( (1.5)^2 \):
\[ (1.5)^2 = 2.25 \]
- Now substitute this back into the volume formula:
\[ V = \pi \times 2.25 \times 6 \]
- Simplifying this gives:
\[ V = \pi \times 13.5 \]
- Using \( \pi \approx \frac{22}{7} \):
\[ V \approx \frac{22}{7} \times 13.5 \approx 42.42 \text{ cubic inches} \]

**Hint:** Make sure to use the correct value of π for accurate calculations.

4. **Determine the total volume of milk available:**
- We know that 1 gallon of milk is equivalent to 231 cubic inches.

**Hint:** Remember the conversion from gallons to cubic inches.

5. **Calculate the number of full glasses that can be filled:**
- To find the number of glasses (N) that can be filled, divide the total volume of milk by the volume of one glass:
\[ N = \frac{\text{Total volume of milk}}{\text{Volume of one glass}} = \frac{231}{42.42} \]
- Performing the division:
\[ N \approx 5.44 \]

**Hint:** When dividing, focus on how many whole glasses can be filled.

6. **Determine the largest number of full glasses:**
- Since Jim can only fill whole glasses, we take the integer part of 5.44, which is 5.

**Hint:** Always round down when dealing with whole items.

### Final Answer:
Jim can pour a maximum of **5 full glasses** of milk from one gallon.