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# Answer to Question #1683 in Calculus for Abhilash

Question #1683
The volume V of a growing spherical cell is given below, where the radius is measured in micrometers (1 &micro;m = 10-6m). Evaluate your answers numerically. (Round the answers to one decimal place.)

(a) Find the average rate of change of V with respect to r when r changes from 5.
(i) 5 to 8 &micro;m &micro;m3 / &micro;m
(ii) 5 to 6 &micro;m &micro;m3 / &micro;m
(iii) 5 to 5.1 &micro;m &micro;m3 / &micro;m
1
2011-02-25T06:38:55-0500
The volume of the sphere is V = 4/3 &pi; r3, thus V changes
(i) from 523.6 &micro;m3 to 2144.7 &micro;m3
(ii) from 523.6 &micro;m3 to 904.8 &micro;m3
(iii) from 523.6 &micro;m3 to 555.6 &micro;m3
The average rate is
(i) (2144.7+523.6)/2 = 1334.1 &micro;m3
(ii) (904.8 + 523.6) /2 = 714.2 &micro;m3
(iii) (555.6 + 523.6)/2 = 539.6 &micro;m3

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