How do you find the volume of a cylinder?

To determine the volume of a cylinder, you need to understand the geometric definition of a cylinder and how its dimensions relate to its volume. The volume of a cylinder is calculated by multiplying the area of its base by its height.

The base of a cylinder is a circle, and the formula for the area of a circle is given by ( A = \pi r^2 ), where ( r ) is the radius of the circle. To find the volume, you then multiply the area of the base by the height ( h ) of the cylinder. Therefore, the correct formula becomes:

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

This matches the correct answer provided, where the volume is expressed as ( V = \pi r^2 h ). This formula effectively captures how the dimensions of the cylinder—its radius and height—contribute to the overall volume, making it fundamental to solving problems involving cylinders. Understanding this relationship is key in geometry and applications involving three-dimensional shapes.