Find the rate of change of the volume of a sphere with respect to its diameter.

Explanation

Volume of a sphere, `(V) = 4/3pir^3`

`=>V = 4/3pi(d/2)^3 = 1/6pid^3`, where `d` is diameter of the sphere.

`:. (dV)/(dd) = 1/6**3pid^2 = pid^2/2`

So, rate of change of the volume of a sphere with respect to its diameter is `(pid^2)/2` cubic units.