(a) The volume of a growing spherical cell is V = 4/3r 3 , where the radius...

(a) The volume of a growing spherical cell is V = 4/3πr³, where the radius r is measured in micrometers (1 μm = 10^-6 m). Find the average rate of change of V with respect to r when r changes from
(i) 5 to 8 μm (ii) 5 to 6 μm (iii) 5 to 5.1 μm
(b) Find the instantaneous rate of change of V with respect to r when r = 5 μm.
(c) Show that the rate of change of the volume of a sphere with respect to its radius is equal to its surface area. Explain geometrically why this result is true. Argue by analogy with Exercise 13(c).