Lesson 2: 6.2 Volumes

- What shape will be formed when we rotate (infinitely fast) an estimating rectangle?
- How do we calculate the volume of this resulting shape as opposed to simply finding the area?
- What expression(s) can we use for the radius/radii?
- Is there any symmetry that can be used to simplify the integral?

- solid of revolution
- axis of rotation

(calculate volume using integrals)

Calculate the volume of a solid of revolution.
DOK levels 1-4

- Designing rotational components like engine pistons, gears, axles, and pressure vessels.
- Determining the fuel capacity of airplane wing tanks, which are often shaped by rotating a curve.
- Creating 3D representations of internal organs by analyzing cross-sectional slices.
- Estimating the volume of materials for structures with rotational symmetry, such as columns, silos, or swimming pools.

Students often have difficulty visualizing the 3-dimensional shapes that are formed by rotating an enclosed region about an axis.

homogeneous grouping and whole-class discussion

section assessment

problems assigned from book