To find the volume of a sphere, which formula should be used?

The volume of a sphere is calculated using the formula ( \frac{4}{3} \pi r^3 ), where ( r ) is the radius of the sphere. This formula is derived from integral calculus and specific geometric considerations regarding the properties of spheres. The term ( r^3 ) indicates that the volume increases with the cube of the radius, reflecting how a three-dimensional object occupies space.

This relationship between radius and volume is significant because it means that even small changes in the radius result in much larger changes in volume, which is important for various applications in math and science, including physics and engineering. Understanding this formula is essential for solving problems that involve spheres in both academic contexts and real-world scenarios.

The other options provided do not represent the correct formula for volume. For example, using the squared radius would apply to calculating the area of a circle, not the volume of a sphere. Hence, the correct choice emphasizes the three-dimensional nature of the sphere and accurately accounts for how volume is computed in three-dimensional space.