Chapter 6.7, Problem 41ES

Use the Theorem of Pappus and the fact that the area of an ellipse with semiaxes $a$ and $b$ is $\pi ab$ to find the volume of the elliptical torus generated by revolving the ellipse

$\frac{{\left(x-k\right)}^2}{a^2}+\frac{y^2}{b^2}=1$

about the $y\text{-axis}$ . Assume that $k>a$ .