What is the formula for the volume of a cylinder?

The volume of a cylinder is determined by the area of its base multiplied by its height. The base of a cylinder is a circle, and the area of a circle is calculated using the formula A = πr², where r is the radius of the circle.

To find the volume (V) of the cylinder, you multiply the area of the base (πr²) by the height (h) of the cylinder. This results in the formula V = πr²h.

This formula effectively captures how the volume changes with variations in both the height of the cylinder and the radius of the base. As either the radius or height increases, the volume increases proportionately, reinforcing the relationship between three-dimensional space and its constituent two-dimensional area.

The other provided options either alter these dimensions incorrectly or introduce unnecessary factors that do not adhere to the correct mathematical relationship for a cylinder's volume.