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1. Consider the region E formed by removing from a hemisphere of radius 1, center the origin, a hemisphere of radius a, center the origin. a.) Find the centroid (x-bar,y-bar,z-bar) of E. Why is xbar=ybar=0 b.) Find the value of a such that zbar=a. That is, set zbar=a and obtain a cubic equation in a. Plot the cubic on your graphing calculator and use 2nd Calc, zero to find the root of the cubic. C.) Explain the physical significance of this centroid.

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1. Consider the region E formed by removing  from a hemisphere of radius 1, center the origin, a hemisphere of

radius a, center the origin. 

a.) Find the centroid (x-bar,y-bar,z-bar) of E. Why is xbar=ybar=0

b.) Find the value of a such that zbar=a. That is, set zbar=a and obtain a cubic equation in a. Plot the cubic on your graphing calculator and use 2nd Calc, zero to find the root of the cubic. 

C.) Explain the physical significance of this centroid. 

 
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