Find the area $of$ the surface generated $by$ revolving the curve about the indicated axis. $y$ equals one sixteenth left parenthesis $x$ squared plus $1$ right parenthesis

$,0$ less than $or$ equals $x$ less than $or$ equals StartRoot $15$ EndRoot $,y-$axis

First set $up$ the integral that gives the area $of$ the given surface. Select the correct choice below and fill $in$ the answer boxes $to$ complete your choice.

$(Type$ exact answers, using $pias$ needed.$)$