Which equation represents the volume of a sphere?

The formula for the volume of a sphere is derived from integral calculus and geometric principles. The correct equation, represented by 4/3πr^3, captures the three-dimensional nature of a sphere. In this formula, "r" represents the radius of the sphere, which is the distance from the center to the surface.

The factor 4/3 arises from the integration needed to calculate the volume of a sphere as it involves curved surfaces rather than flat dimensions. This formula indicates that as the radius increases, the volume increases significantly due to the cube (r^3) term. Consequently, when considering spheres of various sizes, even a small increase in radius leads to a large increase in volume, highlighting the importance of using the correct formula.

Other candidates present alternative mathematical relationships but do not apply to sphere volume. For example, the one involving πr^2h corresponds to the formula for the volume of a cylinder, where "h" represents height in addition to the base area (circle). Similarly, while the equation 2πrh represents the lateral surface area of a cylinder, it misses out on any volume calculations altogether. The formula πr^3 is not dimensionally accurate for volume; instead, it lacks the necessary factor to