What is the formula for the volume of a cylinder?

The formula for the volume of a cylinder is V = πr²h, where V represents the volume, r is the radius of the circular base, and h is the height of the cylinder. This formula is derived from the fact that the volume of a cylinder is essentially the area of its base multiplied by its height.

To break it down further, the area of the circular base of the cylinder is calculated as A = πr². Since a cylinder extends this base vertically up to height h, the overall volume can be found by multiplying the area of the base by the height: V = area × height = πr² × h. This relationship is fundamental in geometry when calculating volumes of three-dimensional shapes.

The other options provided do not accurately represent the volume of a cylinder. For instance, adding factors like 2 or incorporating diameter (d) instead of radius (r) leads to incorrect formulas that misrepresent how volume should be calculated for a cylinder. Thus, the correct representation of a cylinder's volume is succinctly captured in the formula V = πr²h.