Surface of Revolution: under xy=9 and to the right of x=1

[Snowdog2112]

Show that when the portion R of the plane under x*y=9 and to the right of x=1 is revolved about the x-axis the volume generated is 81pi cu. in. but the area of the surface is infinite.

I have absolutely no idea how to get this one going, and I couldn't find anything like it in the book.

 

[galactus]

Washers:

\(\displaystyle \L\\{\pi}\int_{1}^{\infty}(\frac{9}{x})^{2}dx\)


Surface of revolution:

\(\displaystyle \L\\2{\pi}\int_{1}^{\infty}(\frac{9}{x}\sqrt{1+\frac{81}{x^{4}}})dx\)