How can I tell which to use (to find volume) without seeing a graph or graphing a bunch of points? Is it possible to look at the x or y intercept?

In another scenario, what if it said the graph should be revolved around y = 10. However, in this case finding a x intercept wouldn't work. How could you tell algebraically if the graph touched y = 10, or not?

How about in this example:

about y = 10, but we don't know if it touches the y = 10 (part of the x axis).

Area