Let $R$ be the region bounded by the graphs of $y=x, y=-x+6$, and the $x$-axis. Select the best method to find the volume of the solid of revolution generated by revolving $R$ about the $x$-axis. Select the correct answer below: Shell Method, integrating with respect to $x$ Shell Method, integrating with respect to $y$ Washer Method, integrating with respect to $x$ Washer.Method, integrating with respect to $y$

Step 1 ：Let $R$ be the region bounded by the graphs of $y=x$, $y=-x+6$, and the $x$-axis. We are asked to find the volume of the solid of revolution generated by revolving $R$ about the $x$-axis.

Step 2 ：The region R is bounded by the lines $y=x$, $y=-x+6$, and the $x$-axis. When this region is revolved about the $x$-axis, the resulting solid is a cone with a smaller cone removed from its center.

Step 3 ：This is a typical example of a problem that can be solved using the Washer Method. The Washer Method is used when the volume of revolution has a hole or gap in the middle, which is the case here.

Step 4 ：Since we are revolving around the x-axis, it would be easier to integrate with respect to x. This is because the radii of the washers in the resulting solid can be expressed as functions of x.

Step 5 ：Let's define the variables: $x = x$, outer_radius = $6 - x$, inner_radius = $x$, height = $3$, volume = $54\pi$.

Step 6 ：Final Answer: The best method to find the volume of the solid of revolution generated by revolving $R$ about the $x$-axis is the \(\boxed{\text{Washer Method, integrating with respect to } x}\).