A laboratory supply company produces graduated cylinders, each with an internal radius of 2 inches and an internal height between 7.75 inches and 8 inches. What is one possible volume, rounded to the nearest cubic inch, of a graduated cylinder produced by this company?

Explanation

To find the volume of a graduated cylinder produced by the laboratory supply company, we will use the formula for the volume of a cylinder:

\[ V = \pi r^2 h \]

where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height.

### Step 1: Identify the given values
The internal radius \( r \) of the graduated cylinder is given as 2 inches. The height \( h \) can vary between 7.75 inches and 8 inches.

### Step 2: Calculate the volume for the minimum height
We will first calculate the volume using the minimum height of 7.75 inches.

Using the formula:

\[ V_1 = \pi (2)^2 (7.75) \]

Calculating \( r^2 \):

\[ r^2 = 2^2 = 4 \]

Now substituting into the volume formula:

\[ V_1 = \pi \cdot 4 \cdot 7.75 \]

Using \( \pi \approx 3.14 \):

\[ V_1 = 3.14 \cdot 4 \cdot 7.75 \]

Calculating the product:

\[ V_1 = 3.14 \cdot 31 = 97.34 \text{ cubic inches} \]

### Step 3: Calculate the volume for the maximum height
Next, we will calculate the volume using the maximum height of 8 inches.

Using the formula:

\[ V_2 = \pi (2)^2 (8) \]

Again, \( r^2 = 4 \):

\[ V_2 = \pi \cdot 4 \cdot 8 \]

Using \( \pi \approx 3.14 \):

\[ V_2 = 3.14 \cdot 4 \cdot 8 \]

Calculating the product:

\[ V_2 = 3.14 \cdot 32 = 100.48 \text{ cubic inches} \]

### Step 4: Determine the range of possible volumes
The volume of the graduated cylinder can range from the minimum volume \( V_1 \) to the maximum volume \( V_2 \):

- Minimum volume: \( 97.34 \) cubic inches
- Maximum volume: \( 100.48 \) cubic inches

### Step 5: Round to the nearest cubic inch
Now we round the volumes to the nearest cubic inch:

- Minimum volume rounded: \( 97 \) cubic inches
- Maximum volume rounded: \( 100 \) cubic inches

### Conclusion
The possible volume of a graduated cylinder produced by this company can be any integer value between 97 and 100 cubic inches, inclusive. Therefore, one possible volume, rounded to the nearest cubic inch, is:

**98 cubic inches.**