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...Calculus ii un section midterm practice problems with answers semon rezchikov posted march thegoal of this assignment is to give you a few more miscellaneous for the rst these will be harder than on similar avor problem take ball radius b centered at zero remove all points from sphere that are distance less x axis set such cylinder picture drawn below here circle crossection and large what volume resulting solid solution gure revolution associated rotating region in xy plane along we use washer method intersecting looking only part positive y value get described by i e inside outside rectangle two conditions correspond being but think outer farther cure as graph function f while inner g curves intersect values solving equation using formula z dx leave it integral note integrand always nonnegative over integration which makes sense because also make need sensible since otherwise after cutting out ve removed whole consider curve length portion lying area surface obtained revolving about ...