How do you calculate the volume of a sphere?

To calculate the volume of a sphere, the correct formula incorporates both the constant pi and the radius of the sphere raised to the third power, modified by the fraction four-thirds. This is mathematically expressed as four-thirds times pi times the radius cubed.

The reasoning behind the use of this formula lies in the geometric properties of a sphere. The volume reflects how much space the sphere occupies and is derived from integral calculus, where the sphere can be conceptualized as a solid shape composed of an infinite number of infinitesimally thin circular disks stacked upon each other. The formula accounts for the sphere's three-dimensional nature, as cubing the radius allows for the volume to appropriately scale with changes in radius.

In terms of practical application, if you know the radius of a sphere, you can easily plug that value into this formula to find the volume. For instance, if the radius is 3 units, the volume can be calculated as four-thirds times pi times 3 cubed, yielding a clear and concise result for the sphere’s capacity.