To find the volume of a cylinder (which is the shape of a water bottle), you can use the formula:
\[ V = \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height, and
- \( \pi \) (pi) is approximately 3.14.
Given:
- Height (\( h \)) = 16 inches
- Radius (\( r \)) = 4 inches
- \( \pi \) = 3.14
Now, plug in the values:
\[ V = 3.14 \times (4^2) \times 16 \]
First, calculate \( 4^2 \):
\[ 4^2 = 16 \]
Now, substitute back into the volume formula:
\[ V = 3.14 \times 16 \times 16 \]
Next, calculate \( 16 \times 16 \):
\[ 16 \times 16 = 256 \]
Now multiply by \( 3.14 \):
\[ V = 3.14 \times 256 \]
Calculating that gives:
\[ V = 803.84 \]
Thus, the volume of the water bottle is:
\[ \boxed{803.84} \text{ cubic inches} \]