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 is essentially composed of two circular bases connected by a curved surface. The formula V = πr²h captures these elements perfectly.

In this formula, πr² represents the area of the circular base, where 'r' is the radius of the base. This area is multiplied by 'h', the height of the cylinder, to account for the three-dimensional space the cylinder occupies. Hence, the total volume is determined by how much space is contained within the circular base multiplied along the height of the cylinder.

In contrast, other formulas listed relate to different shapes or geometric concepts. The formula involving 2πr² would be more appropriate for calculating surface area, while lwh is the volume formula for a rectangular prism. Lastly, the formula 1/3πr²h applies to the volume of a cone, which tapers to a point rather than maintaining a consistent circular cross-section throughout its height. Thus, when identifying the volume of a cylinder, V = πr²h is the appropriate and correct choice.