The formula for the volume \( V \) of a cylinder with radius \( r \) and height \( h \) is given by:
\[ V = \pi r^2 h \]
To informally argue for this formula, consider that a cylinder can be thought of as a series of circular slices stacked on top of one another. The area of a single circular slice is \( \pi r^2 \), as it represents the area of the base circle. When you multiply this area by the height \( h \), you effectively fill the cylinder with these circular areas from the bottom to the top, resulting in the formula \( V = \pi r^2 h \). Thus, the volume of the cylinder is the product of the area of its base and its height.