What is the formula for the volume of a cylinder?

The formula for the volume of a cylinder is derived from the area of the base and the height of the cylinder. A cylinder has a circular base, and the area of a circle is calculated using the formula A = πr², where r is the radius of the base. To find the volume of the cylinder, you multiply the area of the base (πr²) by the height (h) of the cylinder. Thus, the overall formula for the volume becomes Volume = πr²h. This formula effectively takes into account the size of the base (as determined by the radius) and how tall the cylinder stretches vertically (the height).

The other answers provided either represent other geometric shapes or formulas that do not apply to a cylinder. For example, the formula for the volume of a rectangular prism is lwh, which involves length, width, and height instead of a cylindrical context. Similarly, the formulas involving 2πrh and πr³ do not accurately describe the volume of a cylinder either. Hence, the correct understanding of how to derive the volume of a cylinder confirms that πr²h is indeed the right choice.