How is the volume of a cylinder calculated?

The volume of a cylinder is calculated using the formula that involves the area of the base and the height of the cylinder. The base of a cylinder is a circle, and the area of a circle is given by the formula ( \pi \times r^2 ), where ( r ) is the radius. To find the volume of the cylinder, you then multiply the area of the base by the height of the cylinder.

Specifically, the volume ( V ) can be expressed as:

[ V = \text{Base Area} \times \text{Height} ]

[ V = (\pi \times r^2) \times h ]

[ V = \pi \times r^2 \times h ]

This formula captures the necessary components for calculating volume: the circular base's area and the height extending vertically from the base. Understanding this concept is crucial for solving problems related to three-dimensional shapes.

The other options either misinterpret the components involved in calculating a cylinder's volume or apply formulas relevant to different geometric shapes.