To find the volume of a cylinder, you 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, and \( \pi \) is approximately 3.14.
In this case, we have:
- Base radius \( r = 4 \) meters
- Perpendicular height \( h = 7 \) meters
Now, substituting these values into the formula:
\[ \text{Volume} = 3.14 \times (4^2) \times 7 \] \[ = 3.14 \times 16 \times 7 \] \[ = 3.14 \times 112 \] \[ = 351.68 \]
Thus, the volume of the cylinder is:
\[ \text{Volume} \approx 351.68 , \text{cubic meters} \]
Rounding to the nearest hundredth, the final answer is:
\[ \boxed{351.68} \] cubic meters.