Lesson 2: 8.2 Area of a Surface of Revolution

- How does area of a surface of revolution differ from surface areas we have found in Geometry?
- How is the surface area formula related to the arc length formula? How is it related to other formulas you remember from Geometry?
- How do we account for the surface being formed by rotating about a vertical axis versus a horizontal axis?

- surface of revolution

(finding area of a surface of revolution)

- Determine the area of a surface of revolution
- DOK Levels 1-4

- calculate amount of material needed for objects with rotational symmetry
- Used in designing the optimal shape of cars, aircraft components, or submarines to minimize drag by analyzing the surface area
- Crucial for designing containers to minimize material usage while maximizing product protection, such as calculating the surface area for specialized food packaging to reduce oxidation

Students may get confused when setting up the integral for a surface formed by rotating about a vertical axis.

Homogeneous grouping and whole class discussion

section assessment

problems assigned from book