# Area & Volume

Curriculum Modules: Volumes of Solids by Revolution by the College Board (pdf - 16 pages)

1) Total Area

• Explanation:

• Practice Problems:

2) Area between curves with respect to dx:

3) Area between curves with respect to dy:

• Explanation:

• Practice Problems:

4) Area between curves: Mixed Review

5) Volume by cross section:

6) Volume: Revolved about the x-axis:

7) Volume: Revolved about the y-axis:

8) Volume: Revolved about any horizontal or vertical lines

• Explanation:

9) Mixed Volume: Review

10) Review

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)

11) Cumulative Review