Question

How do you find the instantaneous rate of change for the volume of a growing spherical cell given by `v = (4/3) (pi) r^3` when r is 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`

:-)