Description
This lesson covers the techniques needed to find the volume of a solid of revolution using cylindrical shells. Rotations about both the x- and y-axes are considered, as well as rotations about a line. Volumes using disks and washers are covered in a separate lesson.
This lesson is appropriate for both AP Calculus AB and BC, as well as college calculus. Note that while finding volumes using cylindrical shells is not explicitly tested on the AP exam, students can earn full credit by using the method. Also, it is something they would likely see in a college calculus course.
Detailed answer keys are included.
The topics covered include:
-Volume of a Cylindrical Shell
-Using Cylindrical Shells to Find Volume
-Rotating About the y-axis
-Rotating About the y-axis
-Rotations About a Line
-Choosing the Best Method
In this product, you will find the following:
-Powerpoint Presentation (30 slides)
-Guided Notes (4 pages, a "filled in" copy is also included)
-Do Now Slips (4 slips on one page, answers included)
-Exit Ticket Slips (4 slips on one page, answers included)
-Homework Assignment (2 pages, a detailed answer key is included)
This lesson is part of a larger unit on Areas and Volumes. The complete unit includes the following:
-Areas Between Curves
-Volumes by Disks
-Volumes by Washers
-Volumes by Cross Sections
-Volumes by Cylindrical Shells
Save money and buy all five lessons as a bundle:
-Areas and Volumes Unit Bundle
This lesson is appropriate for both AP Calculus AB and BC, as well as college calculus. Note that while finding volumes using cylindrical shells is not explicitly tested on the AP exam, students can earn full credit by using the method. Also, it is something they would likely see in a college calculus course.
Detailed answer keys are included.
The topics covered include:
-Volume of a Cylindrical Shell
-Using Cylindrical Shells to Find Volume
-Rotating About the y-axis
-Rotating About the y-axis
-Rotations About a Line
-Choosing the Best Method
In this product, you will find the following:
-Powerpoint Presentation (30 slides)
-Guided Notes (4 pages, a "filled in" copy is also included)
-Do Now Slips (4 slips on one page, answers included)
-Exit Ticket Slips (4 slips on one page, answers included)
-Homework Assignment (2 pages, a detailed answer key is included)
This lesson is part of a larger unit on Areas and Volumes. The complete unit includes the following:
-Areas Between Curves
-Volumes by Disks
-Volumes by Washers
-Volumes by Cross Sections
-Volumes by Cylindrical Shells
Save money and buy all five lessons as a bundle:
-Areas and Volumes Unit Bundle
Report this resource to TPT
Reported resources will be reviewed by our team. Report this resource to let us know if this resource violates TPT's content guidelines.
Highlights
Digital downloads
Grades
10th - 12th, Higher Education
Subjects
Tags
Pages
45
Answer Key
Included
Teaching Duration
50 minutes
Save even more with bundles
This bundle includes five lessons which make up Unit 8: Areas and Volumes. These lessons are appropriate for AP Calculus AB, AP Calculus BC, or college calculus.Each lesson includes a PowerPoint presentation along with guided notes, a Do Now, an Exit Ticket, and a homework assignment. All componen
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This is a set of resources for a full AP Calculus AB curriculum.Each lesson contains a set of guided notes (with a filled-in version), a set of Powerpoint slides to go along with the notes, a Do Now and an Exit Ticket, and a homework assignment (with solutions).The lessons are broken up into 8 units
Price $375.00Original Price $424.00Save $49.00
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Description
This lesson covers the techniques needed to find the volume of a solid of revolution using cylindrical shells. Rotations about both the x- and y-axes are considered, as well as rotations about a line. Volumes using disks and washers are covered in a separate lesson.
This lesson is appropriate for both AP Calculus AB and BC, as well as college calculus. Note that while finding volumes using cylindrical shells is not explicitly tested on the AP exam, students can earn full credit by using the method. Also, it is something they would likely see in a college calculus course.
Detailed answer keys are included.
The topics covered include:
-Volume of a Cylindrical Shell
-Using Cylindrical Shells to Find Volume
-Rotating About the y-axis
-Rotating About the y-axis
-Rotations About a Line
-Choosing the Best Method
In this product, you will find the following:
-Powerpoint Presentation (30 slides)
-Guided Notes (4 pages, a "filled in" copy is also included)
-Do Now Slips (4 slips on one page, answers included)
-Exit Ticket Slips (4 slips on one page, answers included)
-Homework Assignment (2 pages, a detailed answer key is included)
This lesson is part of a larger unit on Areas and Volumes. The complete unit includes the following:
-Areas Between Curves
-Volumes by Disks
-Volumes by Washers
-Volumes by Cross Sections
-Volumes by Cylindrical Shells
Save money and buy all five lessons as a bundle:
-Areas and Volumes Unit Bundle
This lesson is appropriate for both AP Calculus AB and BC, as well as college calculus. Note that while finding volumes using cylindrical shells is not explicitly tested on the AP exam, students can earn full credit by using the method. Also, it is something they would likely see in a college calculus course.
Detailed answer keys are included.
The topics covered include:
-Volume of a Cylindrical Shell
-Using Cylindrical Shells to Find Volume
-Rotating About the y-axis
-Rotating About the y-axis
-Rotations About a Line
-Choosing the Best Method
In this product, you will find the following:
-Powerpoint Presentation (30 slides)
-Guided Notes (4 pages, a "filled in" copy is also included)
-Do Now Slips (4 slips on one page, answers included)
-Exit Ticket Slips (4 slips on one page, answers included)
-Homework Assignment (2 pages, a detailed answer key is included)
This lesson is part of a larger unit on Areas and Volumes. The complete unit includes the following:
-Areas Between Curves
-Volumes by Disks
-Volumes by Washers
-Volumes by Cross Sections
-Volumes by Cylindrical Shells
Save money and buy all five lessons as a bundle:
-Areas and Volumes Unit Bundle
Report this resource to TPT
Reported resources will be reviewed by our team. Report this resource to let us know if this resource violates TPT's content guidelines.
Reviews
All verified TPT purchases
Very nice and engaging lesson. I used it with my students.
Thank you!
This was a great way to introduce a topic that is need for calc two but not on the AP test. It is beneficial to students moving on to calculus two in college but took AB calculus in high school.
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