What is the formula for the volume of a cylinder?

The formula for the volume of a cylinder is derived from its geometric properties. A cylinder consists of two circular bases and a height that connects these bases. The volume formula is formulated by calculating the area of one of the circular bases and then multiplying it by the height of the cylinder.

The area of a circle is calculated using the formula (A = \pi r^2), where (r) is the radius of the base. Once you have the area of the base, multiplying it by the height (h) of the cylinder gives you the volume (V) of the cylinder. This relationship can be expressed mathematically as:

[ V = \text{Area of base} \times \text{Height} = \pi r^2 \times h ]

Thus, putting it all together, the volume of a cylinder can be succinctly represented as (V = \pi r^2 h), confirming that this option accurately represents the formula. The other choices involve incorrect combinations or formulations of the radius, height, and constants, which do not conform to the standard formula for the volume of a cylinder.