What is the formula for the volume of a cylinder?

The formula for the volume of a cylinder is given by πr²h, where r is the radius of the base of the cylinder and h is the height of the cylinder. This formula works because the volume of a cylinder can be thought of as the area of its circular base (which is calculated as πr²) multiplied by its height (h).

When you calculate the area of the circular base, you're determining how much space that base occupies. By then extending this area vertically through the height of the cylinder, you effectively fill the three-dimensional space of the cylinder, which gives you the total volume.

The other provided choices correspond to different geometric figures or concepts: one formula represents the volume of a sphere, another describes the area of a triangle, and the last one is related to the volume of a rectangular prism. Each of these has its own specific context and application that is distinct from that of a cylinder.