The volume of a sphere is giving by volume equals pi times diameter cube divided by 4 (v=3.14d^3/4) where v is the volume and d is the diameter of the sphere. (Using the SI Units analysis)



v=3.14d^3/4

well, volume is measured in m^3 and d is measured in m, since you're cubing d, that forms m^3, so the dimensions are the same on both sides.

The equation is dimensionally correct, but the denominator is wrong. The volume of a sphere is (4/3) * pi * Radius^3. Expressed in terms of the diameter D, the volume is:


V = \frac {\pi D^3} 6