Which formula represents the volume of a cylinder?

The formula for the volume of a cylinder is expressed as V = πr²h. This formula indicates that the volume (V) is calculated by multiplying the area of the base of the cylinder, which is a circle, (represented by πr² where r is the radius), by the height (h) of the cylinder.

In this context, πr² gives the area of the circular base, while multiplying it by the height effectively stacks that base across the height of the cylinder, resulting in the total volume. This relationship highlights how the dimensions of both the base and height directly contribute to the overall capacity of the cylinder.

The other options represent different geometric shapes or formulas. For instance, the formula mentioned in option B relates to the surface area of a cylinder and not its volume. The option C describes the volume of a sphere, where r is the radius of the sphere, and option D—though it resembles the formula for a cylinder—incorrectly uses diameter (d) instead of radius (r), which makes it inaccurate for calculating cylindrical volume.