When integrating using shells, the first step is to plot the graph. I personally plotted it with the x and y axis switched, because it aids me in picturing the graph. The integral ranges from 9 to 11, since those are the limits from the two lines y = 9 and y = 11. The reason that these are the limits is because it is rotating around the x, not the y.
 intlimits^{11}_{9}
Now that you have the limits of the integral, you have to find what goes inside it. 
Because you are integrating using shells, you need to remember to include the 2pi y Again, there is a y here instead of an x, because you are rotating around the x axis. Then you just need to input the function f(y). If you look at the graph that you (hopefully) plotted, you can see that this function ranges between the y axis and the curve f(y) = frac{9}{y}. Put together the pieces, and you have the integral
 intlimits^{11}_{9} {2 pi y*f(y)} , dy
After substituting in f(y) = frac{9}{y}, you get 
 intlimits^{11}_{9} {2 pi y*frac{9}{y}} , dy
Simplified, this is  18piintlimits^{11}_{9} , dy
Integrating, we get  18pi * 2

Therefore, the solution is  36 pi

Note: I didn’t spend very much time reviewing these integrals, so I may be incorrect.