a. Find the center of mass for a quarter of a uniform sphere in terms of the outside radius of the sphere, R. (Figure 1)

b. Find the centroid for an area defined by the equations y=2x+4 and y=(2x−3)^(2)+1. (Figure 2)

c. As shown, a section of a roller coaster track (Figure 3) follows the form of y=(2/3)x^(1.5). Locate the centroid x¯of the track between x=0 m and x=3.5m.

Figure 1 of 3