Answer to Question #7803 in Calculus for cobi

Question

the volume of a growing spherical cell is v=4/3πr^3, where the radius r is measured in micrometers 1 μm=10^-6m. find the rate of change with respect to r when r=5 μm.

Answer 1

The rate of a change is a derivative of the volume with respect to radius:

v'(r) =& (4/3πr³)' = 4/3*3πr² = 4πr².

So, the rate of change with respect to r when r=5 μm is 4π5² = 100π.