The formula for the volume of a cylinder is given by \( V = \pi r^2 h \), where \( r \) is the radius of the base and \( h \) is the height of the cylinder.
An informal argument for this volume formula can be constructed by considering the cylinder as made up of many tiny circular disks stacked on top of each other, each with a thickness \( dh \). The area of each disk is equal to the area of the base of the cylinder, which is \( \pi r^2 \). Therefore, to find the total volume, we multiply the area of the base (\( \pi r^2 \)) by the height of the cylinder (\( h \)), leading to the conclusion that the volume is the product of the base area and height, or \( V = \pi r^2 h \). This reasoning aligns with our understanding of how area and height combine to fill the three-dimensional space of the cylinder.