Question

How o do you determine the instantaneous rate of change of `V(r) = 4/3πr^3` for `r= 5`?

Answer 1

Firs evaluate the derivative of your volume (with respect to `r`:
`V'(r)=(dV(r))/(dr)=(4/3)pi*3r^2`
Now substitute `r=5` in it:
`V'(5)=(4/3)pi*3*25=100pi`

:-)