Question 250791
formula in terms of radius is:


v = (4/3) * pi * r^3


radius equals diameter divided by 2:


r = d/2


replace r with (d/2) to get:


v = (4/3) * pi * (d/2)^3


(d/2)^3 is the same as (1/2)^3 * d^3 so your equation becomes:


v = (4/3) * pi * (1/2)^3 * d^3 which becomes:


v = (4/3) * pi * (1/8) * d^3


simplify to get:


v = (1/6) * pi * d^3


example:


let d = 16


that makes r = 8


v = (4/3) * pi * r^3 = (4/3) * pi * (8)^3 = (4/3) * pi * 512 = 682.67 * pi


v = (1/6) * pi * d^3 = (1/6) * pi * 16^3 = (1/6) * pi * 4096 = 682.67 * pi


both forms are equivalent, so the formula in terms of d is:


v = (1/6) * pi * d^3