To find the average value of a function f(x, y, z) on a solid region E, we have the formula 1 avg(f) /// f(x, y, z) dV volume(E) E (a) Find a function f(x, y, z) which gives the distance from a point (x, y, z) to the origin (0,0,0). (b) Suppose E is a solid ball of radius 2 centered at the origin. Use the formula above to find the average value of f (from part (a)) on the E. Hint: the volume of a sphere of radius r is V = (c) Is the average distance from a point in E to the origin more or less than half the radius of E?

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A: To find the average value of  over the region .

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A: Note: As you have posted multiple questions but according to guidelines I will answer the first…

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A: Average  value  =1V∫∫∫W f dv

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A: The sketch of the solid region bounded is given below.

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A: Since you have posted multiple questions, we will solve the first question for you. If you want any…