Volume of revolution between y=sinx and y=cosx

How would I go about solving the following problem?

**Find the volume of revolution defined by rotating, around the x-axis, the area between the graphs of y = sinx and y = cosx on the interval where 0 is less than or equal to x, which is less than or equal to 1.**

I'm aware of the formula for calculating solids of revolution, and could solve the problem if it was just the area between y = sinx and the x-axis. I'm also aware of the "washer" method. However, the problem I'm having is that y = sinx and y = cosx cross over each other between 0 and 1, so I don't know how I'm supposed to deduce the formulas for the radius of the inner and outer circle of each washer. Should I be treating them as two different solids of revolution on an interval of 0 to the crossover point and the crossover point to 1? I think this would work, but I doubt it's the correct/best method. Any help would be greatly appreciated.