The volume V of a growing spherical cell is V = 4 3 πr3, where the radius is measured in micrometers (1 µm = 10−6m). Find the average rate of change of V with respect to r when r changes from 6 to each of the following. (Round your answers to one decimal place.) (i) 6 to 9 µm
(ii) 5 to 6 µm
(iii) 5 to 5.1 µm

(i). 715.92 µm^3/ µm

(ii). 380.99 µm^3/ µm

(iii). 320.32 µm^3/ µm

Step-by-step explanation:

In this case we have V (r) = (4/3) * pi * r ^ 3

Average rate change of a function f (x) from x = a to x = b is given by:

deltafm / delta x = [f (b) - f (a)] / (b-a)

Thus:

(i). [V(9) - V(6)]/(9 - 6) =  [(4/3)*3.14*(9)^3 - (4/3)*3.14*(6)^3]/3 = 715.92 µm^3/ µm

(ii). [V(6) - V(5)]/(6 - 5) =  [(4/3)*3.14*(6)^3 - (4/3)*3.14*(5)^3]/1 = 380.99 µm^3/ µm

(iii). [V(5.1) - V(5)]/(5.1 - 5) =  [(4/3)*3.14*(5.1)^3 - (4/3)*3.14*(5)^3]/0.1 = 320.32 µm^3/ µm

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step-by-step explanation:

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