Lesson Plan Ap Calculus Bc printable pdf download

Lesson Plan

AP Calculus BC

Subject/Course:

AP Calculus BC

Grade Level:

11-12

Topic of lesson:

Introduction to volumes of solids

Objective:

Students will develop and understand the process of finding the volume of a solid of revolution.

Materials:

Textbook, Lemon, Knife, Centimeter Graph Paper, and metric ruler, images of solids of

revolution from the text and computer

Procedures:

1. Review the concept of computing the area between curves and describe the process of

revolving these areas around a horizontal or vertical axis. Explore ways to illustrate the solids

formed. Using the document camera and projector, the teacher should show images of the solids

formed by these revolutions.

2. Discuss methods of finding volumes of “non-geometric” shapes. Lead discussion of ideas to

solve the problem of finding the volume of a lemon. Possible ideas: displacement in water,

volume by slicing—maybe even Calculus

3. Place lemon on centimeter graph paper beneath projector and sketch its shape, using x-axis as

axis for lemon. Let class observe this sketch and collect data to use with regression features of

graphing calculator to approximate the “curve of the lemon.”

4. With lemon image being projected, slice the lemon into several “disc shaped” slices. Give

each group of students one slice of the lemon to measure and approximate its volume using the

formula for the volume of a cylinder. Students will share the results of their section with class

and the class will find the sum of all the volumes.

5. Discuss relationship of slices of lemon to the sketch of the “curve of the lemon”. Have

students use the regression feature of their graphing calculators to find a polynomial equation

that fits the curve. Each group will bring their equation to the desk for display. Class will decide

which equation to use.

6. Place a slice of lemon on the sketch of its shape and discuss the relationship of the equation

value and the radius of the lemon slice. Develop the integral that finds the volume.

7. Compare all the findings. Lead discussion comparing the slicing of the lemon to a Riemann

sum and summarize.

Lesson Plan Ap Calculus Bc