For a sphere, what is the formula to calculate the volume?

The volume of a sphere is determined by the formula V = (4/3)πr^3. This formula derives from the mathematical principles of solid geometry, where the volume of three-dimensional objects is calculated by considering their shape and volume scaling with the cube of their radius.

In this formula, 'V' represents the volume of the sphere, 'π' is a constant that represents the ratio of the circumference of a circle to its diameter, and 'r' is the radius of the sphere. The presence of 'r^3' signifies that the volume scales with the cube of the radius, indicating how changes in size impact the overall space enclosed within the sphere.

Understanding the components of this formula provides insight into how we derive volumes for various three-dimensional objects. The factor of (4/3)π ensures that the result appropriately reflects the unique properties of a sphere compared to other geometric shapes, such as cylinders or cubes.

The other alternatives either represent the volume of different shapes or are formulas that pertain to surface area or other mathematical concepts, thereby making them unsuitable for calculating the volume of a sphere.