To determine the value of \( a \) in the given context, let's go through the step-by-step solution for finding the volume of a right circular cylinder and then relate it to the form \( a \pi \).
1. Identify the formula for the volume of a right circular cylinder:
[tex]\[
V = \pi r^2 h
\][/tex]
2. Substitute the given values:
- Radius (\( r \)) = 4 feet
- Height (\( h \)) = 30 feet
3. Substitute these values into the formula:
[tex]\[
V = \pi (4)^2 (30)
\][/tex]
4. Simplify inside the parentheses first:
[tex]\[
V = \pi (16) (30)
\][/tex]
5. Multiply the numbers:
[tex]\[
V = \pi \times 480
\][/tex]
6. Express the volume in terms of \( a \pi \):
[tex]\[
V = a \pi
\][/tex]
By comparing, we can see that \( a = 480 \).
Thus, the value of \( a \) is [tex]\[
\boxed{480}
\][/tex]
