How do you calculate the volume of a sphere?

The volume of a sphere is calculated using the formula ( V = \frac{4}{3} \pi r^3 ). This formula is derived from integral calculus and reflects the three-dimensional nature of a sphere.

The term ( r ) represents the radius of the sphere, which is the distance from the center of the sphere to any point on its surface. By cubing the radius (represented by ( r^3 )), the formula accounts for the three-dimensional space that the sphere occupies. The factor of ( \frac{4}{3} ) ensures that the volume is accurately scaled relative to the area that is encompassed by its surface, represented by the circular cross-sections that the sphere contains.

Other options do not represent the volume of a sphere. For instance, the formula for calculating the area of a circle is given by ( A = \pi r^2 ), which is related to two-dimensional shapes rather than three-dimensional volumes. The expression ( 2\pi r ) corresponds to the circumference of a circle, and ( 4\pi r^2 ) is the formula for the surface area of a sphere, not its volume. Thus, the correct formula for the volume is essential for