SOLUTION: The volume, V, of a sphere is a function of its radius, r, where V = 4/3pir^3. Express the volume as a function of the diameter, d.

Question 250791: The volume, V, of a sphere is a function of its radius, r, where V = 4/3pir^3. Express the volume as a function of the diameter, d.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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

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