Question

the volume of a growing spherical cell is
v=(4/3)(pi)r^3 where radius is measured in micrometers. find the instantaneous rate of change of v with respect to r when r=5um

Answer 1

Rate of change is the same thing as the derivative. So the answer is dv/dr at r=5

Answer 2

The volume of a growing spherical cell is V = 4/3pr^3 where the radius r is measured in micrometers (1 micrometer = 10^-6 m). Find the average rate of change of V with respect to r when r changes from:
(i) 5 to 8 micrometers
(ii) 5 to 6 micrometers
(iii) 5 to 5.1 micrometers