AP Calculus volume problems

Mike May, Mar 17, 2016

A collection of applets written by Doug Kuhlmann illustrating volume problems from the AP test

Table of Contents

  1. Rectangle Cross Sections
    1. AB2011_3b_B Volumes
    2. AB2010_4c AP volume problem
  2. Semicircle Cross Sections
    1. AB2007_1c Calculus Volumes
  3. Volume By Shells
    1. AB2008_1b_B Volume by Shells
    2. AB2009_4c Volume by Shells
    3. AB2010_4b Volume by Shells
  4. Square Cross Sections
    1. AB2008_1c_B Volume, square cross sections
    2. AB2008_1c Volume square cross section
    3. AB2009_4c Volume square cross sections
    4. AB2009_4b Volume square cross sections
    5. AB2009_4b_B Volume square cross section
    6. AB2010_1c_B Volume square cross section
    7. AB2012_2b Volume square cross sections
    8. AB2013_5c Volume square cross section
    9. AB2014_2b Volume square cross section
    10. AB2015_2b Volume square cross section
  5. Volume by washers
    1. AB2014_2a Volume by washers
    2. AB2013_5b Volumes washers
    3. AB2011_3c Volume by washers
    4. AB2010_4b Volume by washers
    5. AB2009_4c_B Volume by washer
    6. AB2008_1b_B W&S volumes by washer
    7. AB2007_1C_B Volumes by washer
    8. AB2007_1b_Modified Volume by washer
    9. AB2006_1b Volume by washers

1.

Rectangle Cross Sections

Problems where the volume is found with rectangular cross sections.

  • 1. AB2011_3b_B Volumes
  • 2. AB2010_4c AP volume problem

1.1.

AB2011_3b_B Volumes

– Mike May

1.2.

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2.

Semicircle Cross Sections

Volumes of solids with known base and semicircle cross sections

  • 1. AB2007_1c Calculus Volumes

2.1.

AB2007_1c Calculus Volumes

An applet to illustrate AP calculus problems AB 2007 1c[br]The applet was written by Doug Kuhlmann
– Mike May

3.

Volume By Shells

A collection of AP calculus problems that look at volume by shells.

  • 1. AB2008_1b_B Volume by Shells
  • 2. AB2009_4c Volume by Shells
  • 3. AB2010_4b Volume by Shells

3.1.

AB2008_1b_B Volume by Shells

An illustration of problem 1b from the AP 2008 calculus test.
– Mike May

3.2.

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4.

Square Cross Sections

A collection of applets illustrating AP exam questions looking at finding volumes by square cross sections

  • 1. AB2008_1c_B Volume, square cross sections
  • 2. AB2008_1c Volume square cross section
  • 3. AB2009_4c Volume square cross sections
  • 4. AB2009_4b Volume square cross sections
  • 5. AB2009_4b_B Volume square cross section
  • 6. AB2010_1c_B Volume square cross section
  • 7. AB2012_2b Volume square cross sections
  • 8. AB2013_5c Volume square cross section
  • 9. AB2014_2b Volume square cross section
  • 10. AB2015_2b Volume square cross section

4.1.

AB2008_1c_B Volume, square cross sections

Problem 1c from the AP 2008 AB test.Applet by Doug Kuhlmann
– Mike May

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5.

Volume by washers

Finding volumes by washers

  • 1. AB2014_2a Volume by washers
  • 2. AB2013_5b Volumes washers
  • 3. AB2011_3c Volume by washers
  • 4. AB2010_4b Volume by washers
  • 5. AB2009_4c_B Volume by washer
  • 6. AB2008_1b_B W&S volumes by washer
  • 7. AB2007_1C_B Volumes by washer
  • 8. AB2007_1b_Modified Volume by washer
  • 9. AB2006_1b Volume by washers

5.1.

AB2014_2a Volume by washers

Problem 2a from AP exam 2014 2aVolume by washersApplet created by Doug Kuhlmann
– Mike May

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5.9.

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