Which formula correctly represents the volume of a sphere?

The volume of a sphere is accurately represented by the formula V = 4/3πr³, where "V" stands for volume and "r" represents the radius of the sphere. This formula derives from integral calculus or geometric principles that consider the three-dimensional nature of a sphere.

The factor π (pi) reflects the relationship of the sphere’s dimensions to circular ones, while the exponent of 3 associated with the radius emphasizes that volume measures three-dimensional space. When you calculate the volume using this formula, you cube the radius, which appropriately accounts for all three dimensions of space occupied by the sphere.

This is a fundamental formula in geometry that illustrates how to determine the capacity of a perfectly round object regardless of its size, as long as you know the radius. The other options do not pertain to the volume of a sphere and are used in different contexts— such as calculating area, triangles, or motion— and thus are not correct in this case.