For each question below, select the cross section shape that gives the correct volume.

All cross sections are parallel $to$ the $y-$axis and perpendicular $to$ the $xy-$plane

Base $Ais$ the region bounded $byy=\sqrt[\phantom{2}]{9-(\frac{x}{2}{)}^2},y=0$

Base $Bis$ the region bounded $byy=3-\frac{x}{2},y=0,x=-6$

$(a)(3$ points$)$ Choose the cross section $so$ that the volume formed $by$ that cross section

with base $Ais$ the same $as$ the volume $of$ base A with the cross section rectangles

$of$ height $2$

$A.$ Squares

$B.45-45-90$ right triangles, one leg $in$ the $xy-$plane

$C.$ Quarter circles

$D.$ Rectangles with height $|x|$

$(b)(3$ points$)$ Choose the cross section $so$ that the volume formed $by$ that cross section

with base $Bis$ the same $as$ the volume $of$ base $B$ with the cross section rectangles

$of$ height $3$

$A.$ Squares

$B.45-45-90$ right triangles, one leg $in$ the $xy-$plane

$C.$ Quarter circles

$D.$ Rectangles with height $|x|$

$(c)(3$ points$)$ Choose the cross section $so$ that the volume formed $by$ that cross section

with base $Ais$ the same $as$ the volume $of$ base $B$ with the cross section rectangles

$of$ height $2$

$A.$ Squares

$B.45-45-90$ right triangles, one leg $in$ the $xy-$plane

$C.$ Quarter circles

$D.$ Rectangles with height $|x|$

$(d)(3$ points$)$ Choose the cross section $so$ that the volume formed $by$ that cross section

with base $Bis$ the same $as$ the volume $of$ base A with the cross section rectangles

$of$ height $4$

$A.$ Squares

$B.45-45-90$ right triangles, one leg $in$ the $xy-$plane

$C.$ Quarter circles

$D.$ Rectangles with height $|x|$