The radius of a spherical balloon is measured as 20 inches, with a possible error of 0.03 inch. Use differentials to approximate the maximum possible error in calculating the following. a) Calculate the volume of the sphere. b) Calculate the surface area of the sphere. c) Calculate the relative errors in part a) and b).

a) , b) , c) , .

Step-by-step explanation:

The volume and the surface area of the sphere are, respectively:

a) The volume of the sphere is:

b) The surface area of the sphere is:

c) The total differentials for volume and surface area of the sphere are, respectively:

Relative errors are presented hereafter:

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step-by-step explanation: