$1.($a$)$ A tent has a elliptical base of equation x $2$ a $2+$ y $2$ b $2=1($a$,$b are measured in meters$)$ and is supported by a horizontal ridge bar held at height c meters above the x$-$axis by vertical supports at the points $($a$,0).$ The material of the tent is stretched tight so that each cross section perpendicular to the ridge bar is an isosceles triangle. Find the volume of the tent. $($b$)$ Set up$,$ but do not evaluate an integral for the volume of the solid obtained by rotating the region bounded by the parabolas y $=8$x $2$x $2,$ y $=4$x $$ x $2$ about $($i$)$ the y$-$axis; $($ii$)$ the line x $=5$; $($iii$)$ the x$-$axis; $($iv$)$ the line y $=3.$