What is the correct formula for the volume of a prism or cylinder?

The formula for the volume of a prism or cylinder is V = A × h, where A represents the area of the base, and h is the height of the prism or cylinder. This formula applies because the volume of a three-dimensional shape can be thought of as the area of its base multiplied by its height.

For a prism, the base can be any polygon, and for a cylinder, the base is a circle. In both cases, the height measurement extends vertically from the base to the top face of the prism or cylinder. The integrity of this formula comes from the fact that the cross-sectional area remains constant as you move along the height.

The other formulas provided relate to different geometric shapes or contexts. For example, one option represents the formula for the volume of a pyramid or cone, which involves taking one-third of the base area times the height. Another option incorrectly involves π and the diameter, which pertains to the surface area or volume of a specific shape, but is not a general formula for prisms or cylinders. The option that simply states V = s × h would apply to a rectangular prism where s represents the length of a side, but does not encompass the general case for all prisms.