What is the formula for calculating the volume of a cylinder?

The formula for calculating the volume of a cylinder is ( \text{Volume} = \pi \times \text{Radius}^2 \times \text{Height} ). This formula is derived from the geometry of a cylinder, which consists of two circular bases and a height that connects them.

To understand why this is the correct formula, consider that the volume of any three-dimensional shape is essentially the space it occupies. For a cylinder, the volume can be thought of as the area of the circular base times the height. The area of the circular base is given by the formula ( \pi \times \text{Radius}^2 ). By multiplying the area of the base by the height of the cylinder, you arrive at the total volume.

This relationship reflects how the height extends the area of the base into a three-dimensional shape, filling up the cylinder's volume. Therefore, using the radius squared ensures that you're accurately calculating the space contained within the cylinder over its height.

Other options either misrepresent the necessary mathematical relationship, like using diameter without correcting for the radius, or omit height, which is crucial for volume calculations in three-dimensional shapes.