Final answer:
The formula 4π r^2 is the formula for calculating the surface area of a sphere, not its volume, radius, or cross-sectional area.
Step-by-step explanation:
The formula 4π r^2 corresponds to the surface area of a sphere with radius r. This can be differentiated from the volume formula for a sphere, which is ⅔(π)(r)³. The formula for the volume of a cube is (s)³ and for the surface area of a cube is 6(s)². Therefore, when discussing the surface area and volume of a sphere, clarity is essential to avoid mixing these up with the formulas for a cube.
When tasked with remembering formulas from geometry, it can be helpful to revert to fundamental geometric principles. For example, a cylinder's volume can be thought of as the area of the circular base multiplied by the height of the cylinder, which reflects a combination of circular and rectangular geometries.
In summary, the given formula, 4π r^2, should not be confused with volume calculations or the dimensions of other shapes such as cubes or cylinders. Instead, it precisely represents the surface area of a sphere.