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

Chapter 3, Problem 16

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(a) The volume of a growing spherical cell is V 4 3r 3 , where the radius r is measured in micrometers (1 m 1026 m). Find the average rate of change of V with respect to r when r changes from (i) 5 to 8 m (ii) 5 to 6 m (iii) 5 to 5.1 m (b) Find the instantaneous rate of change of V with respect to r when r 5 m. (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).

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