Calculus Volume Question

Question

A triangular region in the first quadrant has vertices at the points (2, 1), (2, 7), and (4, 3). Find the volume of the solid of revolution generated by revolving this region around the line x = 2 using the disk/washer method. 

Answer 1

Make it easy on yourself by moving the triangle 2 units toward the y-axis and then use the disk method.and get the same answer. If you revolve around the line x=2, you just have to subtract the volume of revolution between the y-axis and the line x=2.

The total volume of revolution is 8 x pi.

You can verify the answer by computing the volume of revolution using the Pappus Method!