Calculus‎ > ‎

### Area & Volume

 Curriculum Modules: Volumes of Solids by Revolution by the College Board (pdf - 16 pages)1) Total AreaExplanation:Notes | AnnotatedPractice Problems:Area between curves:2)  With respect to dx: Explanation:Notes | AnnotatedKhan Video: Area between curvesKhan Video: Area between curves with multiple boundariesPractice Problems:Worksheet | Answers        3)  With respect to dy: Explanation:Notes | AnnotatedPractice Problems:Worksheet | Answers        4)  Mixed Review  Videos: Hollis: Area Between CurvesPractice Problems:Area Between Curves using dx & dy WS | Answers AP Questions:2005 Q1 - parts a & b2001 Q1 - parts a & b1998 Q1 - parts a and b5) Volume by cross section:Explanation:Perpendicular to the x-axis:Notes | AnnotatedMore examples: Notes | Annotated | videoPerpendicular to the y-axis: Notes | AnnotatedWebsites:Wolfram DemoVideo: Hollis, University of Houston (slides 1-5)Isometric PaperPractice Problems:Volume by revolution:        6)  Revolved about the x-axis: Notes | Annotated        7)  Revolved about the y-axis: Notes | Annotated         8)  Revolved about any horizontal or vertical lines: Notes | Annotated         9)  Mixed ReviewNotes | Annotated | website - text based explanation | website - some animation  Desmos Activity: Volumes by Revolution (teacher use)Practice Problems:Interactive websites:Interactive website: revolution (Shodor - Java)Videos:Hollis, University of HoustonKhan: 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"Khan: Solid of Revolution (part 6) - revolution around the y-axis (x = 0)10) Review 11) Cumulative Review WS | AnswersAP Questions2014 Q2 - Volume by revolution about y = -2; cross sections with right isosceles triangles; equal areas2012 Q2 - area, cross section of different upper limits, two equal regions2011 (Form B) Q3 - area, cross section (rectangle with height 2y)2011 Q3 - area and revolve about y = 1; Khan video: part a & b | part c2010 (Form B) Q1 - area, revolve about y = 8, and cross section2010 Q4 - area, revolve about y = 7, and cross section are rectangles perpendicular to the y-axis2009 (Form B) Q4 - area, cross section, revolve about y = 22009 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-axis2008 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 = 12007 Q1 - area, revolution about x-axis, and cross section (no graphs are provided)2006 (Form B) Q1 - 2 area and revolve about y = - 22006 Q1 - area, revolve about y = - 3 and the y-axis2005 (Form B) Q1 - area, revolve about the x-axis, and cross-section2005 Q1 - 2 area questions and revolve about y = -12004 (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-axis2003 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 section2002 Q1 - area, revolve about y = 4, and minimum (no graphs are provided)2001 Q1 - 2 area questions and one revolve about the x-axis2000 Q1 - area, revolve about the x-axis, and cross section1999 Q2 - area, revolve about the x-axis, and equal volume when divided and revolved1998 Q1 - area, 2 equal areas, revolve about the x-axis, and 2 equal volumes by revolutions (no graphs are provided)