To find the volume of a cylinder (which is the shape of the 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,
- \( \pi \) is approximately 3.14.
Given:
- Height \( h = 16 \) inches,
- Radius \( r = 4 \) inches.
Now, substitute the values into the formula:
\[ V = 3.14 \times (4^2) \times 16 \]
First, calculate \( r^2 \):
\[ r^2 = 4^2 = 16 \]
Now substitute back into the volume formula:
\[ V = 3.14 \times 16 \times 16 \]
Now perform the multiplication:
\[ V = 3.14 \times 256 \]
Now calculate \( 3.14 \times 256 \):
\[ 3.14 \times 256 = 802.56 \]
Therefore, the volume of the water bottle is approximately:
\[ \boxed{802.56} \text{ cubic inches} \]