What formula is used to calculate the volume of a cylinder?

The formula used to calculate the volume of a cylinder is based on the understanding that the volume of a three-dimensional shape can be derived from the area of its base and its height. In the case of a cylinder, the base is a circle. The area of a circle is given by π times the radius squared (π × radius²). To find the volume of the cylinder, you then multiply the area of the base by the height of the cylinder.

Thus, the correct formula for the volume of the cylinder is π × radius² × height. This effectively gives the total space occupied within the cylinder based on how much circular area is available in the base and how tall the cylinder rises.

Other formulas provided do not represent the correct computation for the volume of a cylinder. For example, the formula involving 1/3 is used for the volume of a cone, which has a different shape and structural properties. The formula that includes a simple addition of height does not correctly factor in the area of the base, while another option that has circumference-related terms relates more to surface area rather than volume measurement.