Final answer:
The volume of a sphere is calculated using the formula 4/3 π r³, with r being the sphere's radius. This formula incorporates the radius cubed, indicating three-dimensional space, and the constants 4/3 and π.
Step-by-step explanation:
To find the volume of a sphere, the correct mathematical equation to use is volume = 4/3 π r³, where r represents the radius of the sphere.
This equation derives from the integral of a circular disk's area as it is rotated around the x-axis to form a sphere. To remember this formula, consider that the radius is cubed, indicating a three-dimensional measurement, and is multiplied by both 4/3 and π, the latter being a constant in circular geometries.
As for the surface area, the equation mentioned, 4πr², involves squaring the radius, which points to it being a two-dimensional measurement for the sphere's surface.
Therefore, the equation related to volume is 4/3πr³ and for surface area, it is 4πr².