$[7/14$ Points$]$

Consider the area of the surface generated by revolving the curve on the indicated interval about the $y-$axis.

$y=1-\frac{x^2}{16},0x4$

Using the definition of the area of a surface of a revolution where $y=f(x),$ find the radius $r(x)$ and $f^{\text{'}}(x).$

$f(x)=$

$f^{\text{'}}(x)=,0x4$

Write and evaluate the definite integral that represents the area of the surface generated by revolving the curve ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}dx=$