The volume \( V \) of a cylinder can be calculated using the formula:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14.
In this problem:
- The base radius \( r = 4 \) meters,
- The height \( h = 7 \) meters.
Now, we substitute the values into the formula:
\[ V = 3.14 \times (4)^2 \times 7 \]
Calculating \( (4)^2 \):
\[ (4)^2 = 16 \]
Now we have:
\[ V = 3.14 \times 16 \times 7 \]
Calculating \( 16 \times 7 \):
\[ 16 \times 7 = 112 \]
Now substituting this back into the volume formula:
\[ V = 3.14 \times 112 \]
Now calculate \( 3.14 \times 112 \):
\[ V = 351.68 \]
Therefore, the volume of the cylinder is:
\[ \boxed{351.68} \text{ cubic meters} \]