To find the height \( h \) of the cylinder using the volume formula, we can start with the given formula for the volume \( V \) of a cylinder:
\[ V = \pi r^2 \cdot h \]
You provided the values:
- \( V = 360\pi \)
- \( r = 6 \)
First, we will substitute the known value of \( r \) into the volume formula.
- Calculate the area of the base using the radius:
\[ r = 6 \implies r^2 = 6^2 = 36 \]
- Substitute \( r^2 \) into the volume formula:
\[ V = \pi \cdot 36 \cdot h \]
This simplifies to:
\[ V = 36\pi h \]
- Now set this equal to the provided volume:
\[ 360\pi = 36\pi h \]
- To solve for \( h \), divide both sides by \( 36\pi \):
\[ h = \frac{360\pi}{36\pi} \]
The \( \pi \) cancels out:
\[ h = \frac{360}{36} \]
- Now simplify \( \frac{360}{36} \):
\[ h = 10 \]
Therefore, the height \( h \) of the cylinder is:
\[ \boxed{10} \]