The formula for the volume \( V \) of a cylinder with radius \( r \) and height \( h \) is given by:
\[ V = \pi r^2 h \]
To understand why this formula works, consider that the volume of a cylinder can be thought of as the area of its base (a circle) multiplied by its height. The area of the circular base is \( \pi r^2 \) (where \( \pi \) is approximately 3.14). When you stack this circular area up evenly for the entire height \( h \), you effectively extend this area upwards, resulting in the volume of the cylinder being the base area times the height: \( \pi r^2 \times h \). This reasoning reflects the relationship between the base and the overall three-dimensional shape of the cylinder.