To find the volume of the water bottle, which is in the shape of a cylinder, we 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,
- \( \pi \) is approximately 3.14.
Given:
- Height \( h = 16 \) inches,
- Radius \( r = 4 \) inches.
Substituting the values into the formula:
\[ V = 3.14 \times (4)^2 \times 16 \]
First, calculate \( (4)^2 \):
\[ (4)^2 = 16 \]
Now substitute back into the volume formula:
\[ V = 3.14 \times 16 \times 16 \]
Next, multiply \( 16 \times 16 \):
\[ 16 \times 16 = 256 \]
Now multiply by \( 3.14 \):
\[ V = 3.14 \times 256 \]
Calculating this:
\[ 3.14 \times 256 = 804.16 \]
Therefore, the volume of the water bottle is:
\[ \boxed{804.16} \text{ cubic inches} \]