Allen WolmerSandy Springs, Georgia, US,

October 31, 2014

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Use definite integrals to find the volume of a solid with known cross-sectional area.

- Mathematics > General
- Mathematics > Calculus

- Grade 11
- Grade 12

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Table of Contents

- Applications of Integration: Volumes
- Volumes by: Cross-Section, Revolution, Shells
- The Disk Method for Determining Volume
- The Washer Method for Determining Volume (Rotating About the X-axis)
- The Washer Method for Determining Volume (Rotating About the Y-axis)
- The Washer Method for Determining Volume NOT Rotating About the X- or Y-axis)
- Disk Method
- Disk Method: Example 1
- Disk Method: Example 2
- Washer Method: Intro & Theory
- Washer Method: Example 1
- How to Calculate Volumes
- Volumes of Revolution
- Volumes of Known Cross Sections
- Volume by Parallel Cross Sections; Discs and Washers Exercises
- Volume Exercises
- Volumes of Revolution - Washers and Disks Exercises

Use definite integrals to find the volume of a solid with known cross-sectional area.

Mooculus Calculus Textbook Section Sect 15.1 pp 235-240

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A Youtube Calculus Workbook (Part 1). A guide through a playlist of instructional Calculus Videos.

Section 18.1-3 pp 258-277

The first time you access this link to download the PDF, you will be asked four questions. Any that do not apply to you may be answered using any of the options listed.

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Instructional video from NROC/Hippocampus the Disk Method for Determining Volume from the Phoenix College Collection-Calculus II.

Video duration: 9:49

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Instructional video from NROC/Hippocampus on the Washer Method for Determining Volume (Rotating About the X-axis) from the Phoenix College Collection-Calculus II.

Video duration: 8:22

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Instructional video from NROC/Hippocampus on the Washer Method for Determining Volume (Rotating About the Y-axis) from the Phoenix College Collection-Calculus II.

Video duration: 7:06

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Instructional video from NROC/Hippocampus on the Washer Method for Determining Volume NOT Rotating About the X- or Y-axis) from the Phoenix College Collection-Calculus II.

Video duration: 9:08

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A Firefly Lectures video on this topic.

Video duration: 8:15

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A firefly Lectures video on this topic.

Video duration: 3:55

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A firefly Lectures video on this topic.

Video duration: 8:45

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A Firefly Lectures video on this topic.

Video duration: 5:46

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A Firefly Lectures video on this topic.

Video duration: 6:53

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MIT Open Courseware video lecture on this topic.

Video duration: 49:57

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Calculus applet illustrating this concept. Requires security enabled Java.

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Calculus applet illustrating concept. Requires security enabled Java.

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This set of exercises supports the following Standards of Mathematical Practice

- 1 Make sense of problems and persevere in solving them.
- 2 Reason abstractly and quantitatively.
- 5 Use appropriate tools strategically.
- 6 Attend to precision.
- 7 Look for and make use of structure.
- 8 Look for and express regularity in repeated reasoning.

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Mooculus Calculus Textbook Exercises, Sect 15.1 p 241 (Ans p 255)

This set of exercises supports the following Standards of Mathematical Practice

- 1 Make sense of problems and persevere in solving them.
- 2 Reason abstractly and quantitatively.
- 5 Use appropriate tools strategically.
- 6 Attend to precision.
- 7 Look for and make use of structure.
- 8 Look for and express regularity in repeated reasoning.

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Curriki Rating**'C'** - Curriki rating C**'C'** - Curriki rating

This set of exercises supports the following Standards of Mathematical Practice

- 1 Make sense of problems and persevere in solving them.
- 2 Reason abstractly and quantitatively.
- 4 Model with mathematics.
- 5 Use appropriate tools strategically.
- 6 Attend to precision.
- 7 Look for and make use of structure.

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Curriki Rating**'C'** - Curriki rating C**'C'** - Curriki rating

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