What is the formula for the volume of a sphere?

The formula for the volume of a sphere is given as V = 4/3 π r³, where "V" represents volume, "π" (pi) is a constant approximately equal to 3.14, and "r" is the radius of the sphere. This formula is derived from calculus and geometric principles, specifically involving the integration of circular cross-sections to find the three-dimensional space occupied by the sphere.

In this formula, the term 4/3 reflects the constant factor that accounts for the spherical shape, while r³ represents the radius cubed, indicating that the volume increases as the radius increases. This emphasizes the relationship between the radius and the volume; even a small increase in the radius leads to a significant increase in volume due to the cubic relationship.

As for the other options, none of them correctly express the volume of a sphere. The first option suggests a formula similar to the volume of a cone, the third reflects the area of a circle, while the fourth option features a coefficient that does not correspond to any known geometric volume formula. Thus, the selection of the volume formula as 4/3 π r³ is accurate and aligns with mathematical standards.