Here is the question:

Determine the volume of a solid generated by rotating the triangle with vertices (0,0), (2,0), (1,1) about the line x = 2.

Now, I took the integral route, using the "washer" method (adding the "slices" from y = 0 to 1) and got an answer of 2*pi.

I also noticed that due to the simplicity of the triangle, we can interpret the distance from (0,0) to (1,1) and (1,1) to (2,0) to be sqrt(2) for each line segment. From that, the area of the triangle is [(sqrt(2))^2]/2 = 2/2 = 1

Then, looking at this 2-dimensional triangle "from above", we can multiply the area by 2*pi, resulting in a volume of 2*pi for the solid. A more or less obvious observation, I know, but I thought it might be nice to share this.

Also, if anyone can confirm that the volume is indeed 2*pi, I'd be very grateful!