How is the volume of a cylinder calculated?

The volume of a cylinder is calculated using the formula πr^2height, where 'r' represents the radius of the base of the cylinder, and 'height' is the vertical height of the cylinder. This formula is derived from the concept that the volume of a three-dimensional shape is the area of its base multiplied by its height.

In the case of a cylinder, the base is a circle, and the area of a circle is calculated as π*r^2. By multiplying this area by the height of the cylinder, you obtain the total volume, which represents the amount of space inside the cylinder.

Other formulas presented, while involving π, do not accurately represent the calculation for the volume of a cylinder. The formula using 2πr would instead pertain to the lateral surface area of the cylinder, and using the diameter (d) in a formula without proper adjustments would not yield the correct volume measurement. Therefore, the choice of πr^2*height is the valid and recognized method for calculating a cylinder's volume.