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56. (a) Cell growth The volume of a growing spherical cell is Vr³, where the radius r is measured in micro- meters (1 μm
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56. (a) Cell growth The volume of a growing spherical cell is Vr³, where the radius r is measured in micro- meters (1 μm
56. (a) Cell growth The volume of a growing spherical cell is Vr³, where the radius r is measured in micro- meters (1 μm 10 m). Find the average rate of = change of V with respect to r when r changes from (iii) 5 to 5.1 μm (i) 5 to 8 μm (ii) 5 to 6 μm (b) Find the instantaneous rate of change of V with respect 5 μm. to r when r = (c) Show that the rate of change of the volume of a cell with respect to its radius is equal to its surface area (S = 4πr²). Explain geometrically why this result is true. Argue by analogy with Exercise 55(c).
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