Area & Volume

• Explanation:

  • Notes | Annotated

• Practice Problems:

  • Worksheet | Answers

• Explanation:

  • Notes | Annotated

  • Khan Video: Area between curves

  • Khan Video: Area between curves with multiple boundaries

• Practice Problems:

  • Worksheet | Answers

• Explanation:

  • Notes | Annotated

• Practice Problems:

  • Worksheet | Answers

• • Explanation:

    • Hollis: Area Between Curves

  • Practice Problems:

    • Area Between Curves using dx & dy WS | Answers

    • U-Sub with Indefinite and Definite WS | Answers

    • AP Questions:

      • 2005 Q1 - parts a & b

      • 2001 Q1 - parts a & b

      • 1998 Q1 - parts a and b

• Explanation:

  • Perpendicular to the x-axis:

    • Notes | Annotated

    • More examples: Notes | Annotated | video

    • Perpendicular to the y-axis: Notes | Annotated

  • Websites:

    • Wolfram Demo

  • Video: Hollis, University of Houston (slides 1-5)

  • Isometric Paper

• Practice Problems:

  • Volume by Cross Sections WS #1 | Answers

  • Volume by Cross Sections WS #2 | Answers

  • AP Questions:

    • 2010 Q4 parts a & c

    • 2009 Q4

    • 2008 Q1

• Explanation:

  • Notes | Annotated

  • Khan: Solid of Revolution (part 1) - revolved around the x-axis (y = 0)

  • Khan: Solid of Revolution (part 2) - revolved around the x-axis (y = 0)

  • Khan: Solid of Revolution (part 4) - more revolution around the x-axis (y=0) - "washers"

• Practice Problems:

  • Worksheet | Answer

• Explanation

  • Notes | Annotated

  • Khan: Solid of Revolution (part 6) - revolution around the y-axis (x = 0)

• Practice Problems

  • Worksheet | Answer

• Explanation:

  • Notes | Annotated

• Explanation:

  • Notes | Annotated | website - text based explanation | website - some animation

  • Hollis, University of Houston

  • Interactive website: revolution (Shodor - Java)

• Practice Problems:

  • Worksheet #1 | Answers

  • Worksheet #2 | Answers

  • Desmos Activity: Volumes by Revolution (teacher use)

• Notes

• Review WS | Answers

AP Questions

• 2014 Q2 - Volume by revolution about y = -2; cross sections with right isosceles triangles; equal areas

• 2012 Q2 - area, cross section of different upper limits, two equal regions

• 2011 (Form B) Q3 - area, cross section (rectangle with height 2y)

• 2011 Q3 - area and revolve about y = 1; Khan video: part a & b | part c

• 2010 (Form B) Q1 - area, revolve about y = 8, and cross section

• 2010 Q4 - area, revolve about y = 7, and cross section are rectangles perpendicular to the y-axis

• 2009 (Form B) Q4 - area, cross section, revolve about y = 2

• 2009 Q4 - area & two cross section problems (one is a function and the other is dy)

• 2008 (Form B) Q1 - area, revolved about x = -1, cross-section perpendicular to the y-axis

• 2008 Q1 - 2 area questions and 2 cross sections (one depth is a function)

• 2007 (Form B) Q1 - 2 area questions and one revolve about y = 1

• 2007 Q1 - area, revolution about x-axis, and cross section (no graphs are provided)

• 2006 (Form B) Q1 - 2 area and revolve about y = - 2

• 2006 Q1 - area, revolve about y = - 3 and the y-axis

• 2005 (Form B) Q1 - area, revolve about the x-axis, and cross-section

• 2005 Q1 - 2 area questions and revolve about y = -1

• 2004 (Form B) Q1 - area, revolve about y = 3 and x = 10 (no graph provided)

• 2004 Q2 - area, revolve about y = 2, and cross section (challenging cross section)

• 2003 (Form B) Q1 - area and revolve about the x-axis

• 2003 Q1 - area, revolve about y = 1, and cross section (height is 5 times its base)

• 2002 (Form B) Q1 - area, revolve about the x-axis, and cross section

• 2002 Q1 - area, revolve about y = 4, and minimum (no graphs are provided)

• 2001 Q1 - 2 area questions and one revolve about the x-axis

• 2000 Q1 - area, revolve about the x-axis, and cross section

• 1999 Q2 - area, revolve about the x-axis, and equal volume when divided and revolved

• 1998 Q1 - area, 2 equal areas, revolve about the x-axis, and 2 equal volumes by revolutions (no graphs are provided)

Cumulative Review WS | Answers