Find the volume of a solid generated by rotating the area in the first quadrant between $y=2x+3$ and $y=x^2$ around the axis $x=4.$

$($A$){\displaystyle \underset{0}{\overset{3}{}}}(4+(2x+3{)}^2-x^2)dx$

$($B$){\displaystyle \underset{0}{\overset{3}{}}}(4+x^2-(2x+3{)}^2-x^2)dx$

$($C$)[{\displaystyle \underset{0}{\overset{3}{}}}(4-\sqrt[\phantom{2}]{y}{)}^{2}dy+{\displaystyle \underset{3}{\overset{9}{}}}\{(\frac{y+1}{2}{)}^2-(4-\sqrt[\phantom{2}]{y}{)}^2\}dy]$

$($D$)$