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G Mm G r F=− r G (311) where is the gravitational constant and is a unit vector pointing radially outward The Earth is assumed to be a uniform sphere of mass M The corresponding gravitational field G =×667 10−11 N⋅m2/kg2 rˆ g G, defined as the gravitational force per unit mass, is given by g 2 ˆ GM mr ==− F g r G G (312V 2πradius shellheightdy 2πyF(y) f(y)dy Ex Find the volume of the solid generated by revolving the first quadrant region bounded by y = 8 − x2, y = 2x, and the yaxis, about the yaxis The upper curve is the parabola y = 8 − x2, and y = 2 x is the lower curve Their first quadrant intersection is at (2, 4), therefore,V A TOR G ARA G E ENT R Y M C N A I R F O U N D A T I ON JOGGING TRAI L DONOR W ALLS 1 3 4 5 2 6 10 14 13 12 16 15 15 24 23 26 25 22 19 18 17 11 7 15 27 21 9 8 1 9 Jimi Derrick's Arbor W achovia Securities Se a ting Area Nan c y G Kinder Oak 2 0 Jack C Alexander Plaza Lily Chen F oster Garden 2 1 The Grove and essels the T reehous e 2 2 Evolutionary Reinfo