1. 8.2 Area of a Surface of Revolution
Definition:
If the graph of a continuous function is revolved about a line, the resulting surface is called a surface of revolution
Surface Area of a Frustum of a Cone: L
Axis of Revolution

2. Surface Area: If the curve is rotated about the x-axis
If the curve is rotated about the y-axis
Note:
Use or

3. Examples:
Find the area of the surface obtained by rotating the curve about the x-axis: 1)
Solutions:

4. 2) rotating about the x-axis
Solutions:

5. Find the area of the surface obtained by rotating the curve about the y-axis:3)
Solutions: