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

Question:

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