Which formula represents the volume of a sphere?

The formula representing the volume of a sphere is indeed expressed as (\frac{1}{6} \pi d^3). This formula can also be derived from the more commonly used volume of a sphere formula, which is (\frac{4}{3} \pi r^3), where (r) is the radius of the sphere. Since the diameter (d) is twice the radius ((d = 2r)), by substituting (r) in terms of (d) into the volume equation, you can arrive at the expression involving diameter.

The volume of a sphere quantifies the space within the three-dimensional boundary of the sphere, making this formula essential in applications involving spherical objects. Its derivation through integration or geometric formulas confirms its accuracy for calculating spherical volumes.

The other options pertain to different geometric shapes or formulas that do not apply to spheres. For instance, the first option refers to the volume of a rectangular prism, the third relates to the volume of a cone, and the last one represents a formula for a different geometric concept. Therefore, only the formula for the volume of a sphere correctly reflects its three-dimensional characteristics, confirming that (\frac{1}{6} \