To find the volume of a cylinder, we can use the formula:
\[ \text{Volume} = \pi r^2 h \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14.
Given:
- Base radius \( r = 4 \) meters,
- Height \( h = 7 \) meters.
Substituting the values into the formula:
\[ \text{Volume} = 3.14 \times (4^2) \times 7 \]
Calculating \( 4^2 \):
\[ 4^2 = 16 \]
Now, substitute that back:
\[ \text{Volume} = 3.14 \times 16 \times 7 \]
Calculating \( 16 \times 7 \):
\[ 16 \times 7 = 112 \]
Now multiply by \( \pi \):
\[ \text{Volume} = 3.14 \times 112 \]
Calculating that:
\[ 3.14 \times 112 = 350.68 \]
Rounding to the nearest hundredth, the volume of the cylinder is:
\[ \boxed{350.68} \text{ cubic meters} \]