Answer
a.) $\displaystyle{V=2\pi\int_{-3}^{3}(5-y)\left(4-\sqrt{7+y^2}\right)\ dy}$
b.) $\displaystyle{V=163.02712}$
Work Step by Step
a.)
$\displaystyle{4^2-y^2=7}\\
\displaystyle{y^2=9}\\
\displaystyle{y=-3\qquad y=3}$
$\displaystyle{V=\int_{-3}^{3}\left(2\pi(5-y)\right)\left(4-\sqrt{7+y^2}\right)\ dy}\\
\displaystyle{V=2\pi\int_{-3}^{3}(5-y)\left(4-\sqrt{7+y^2}\right)\ dy}$
b.)
$\displaystyle{V=163.02712}$
