The area of a disk, more commonly called the area of a circle, of radiusr is equal to πr2. Here the symbol π (Greek letter pi) denotes the constant ratio of the circumference of a circle to its diameter or of the area of a circle to the square of its radius. Since the area of a regular polygon is half its perimeter times its apothem, and a regular polygon approaches a circle as the number of sides increase, the area of a disk is half its circumference times its radius (i.e. 1⁄2 × 2πr × r).
History
Modern mathematics can obtain the area using the methods of integral calculus or its more sophisticated offspring, real analysis. However the area of circles was studied by the Ancient Greeks. Eudoxus of Cnidus in the fifth century B.C. had found that the areas of circles are proportional to their radius squared. The great mathematician Archimedes used the tools of Euclidean geometry to show that the area inside a circle is equal to that of a right triangle whose base has the length of the circle's circumference and whose height equals the circle's radius in his book Measurement of a Circle. The circumference is 2πr, and the area of a triangle is half the base times the height, yielding the area πr2 for the disk. Prior to Archimedes, Hippocrates of Chios was the first to show that the area of a disk is proportional to the square of its diameter, as part of his quadrature of the lune of Hippocrates, but did not identify the constant of proportionality.
This calculus video tutorial explains how to use the disk method and the washer method to calculate the volume of a solid when the region enclosed by the curves are rotated around the x axis, y axis, and non axis or another line parallel to the x or y axis. This video contains plenty of examples and practice problems for you to work on. It shows you how to set up and evaluate the definite integral. Techniques include expanding a binomial expression and basic integration rules.
Full 1 Hour 44 Minute Video:
https://www.patreon.com/MathScienceTutor
Direct Link to The Full Video:
https://bit.ly/2V17469
_________________________________
Full 1 Hour 44 Minute Video:
https://www.youtube.com/watch?v=7CMTMCS0Zq0
Join The Membership Program:
https://bit.ly/46xaQTR
published: 04 Jan 2021
5 Area of disc with animation by 3 different methods
There can not only be just one differential element for a particular uniform rigid body but more.Here we demostrate how to find the area of a disc using differential elements method in 3 different ways using animations
published: 10 Aug 2019
Electric Field from a Ring and a Disk
Physics Ninja looks at the problem of calculating the electric field from a ring and disk by integration. The ring and the disk are uniformly charged the field is calculated for a point on the axis.
published: 21 Feb 2022
Unit 7 Lesson 4 Proving the Area of a Disk Notes
This project has been created with Explain Everything™ Interactive Whiteboard for iPad
published: 07 May 2016
Physics 36 The Electric Field (9 of 18) Disc of Charge
Visit http://ilectureonline.com for more math and science lectures!
In this video I will find the electric field of a disc of charge.
published: 23 Mar 2014
Disk, Washer and Shell Methods- Volume of Solid of Revolution
In this video, I showed how to find the volume of Solid of Revoltion using Disk, Washer and Shell methods
published: 14 Dec 2022
Disk/Washer vs. Cylindrical Shell...when to use which?
There are two ways to find the volume of three dimensional objects in calculus: the disk washer method and the cylindrical shell method.
What is the disk washer method? What is the cylindrical shell method? That's exactly what I'm going to talk about today. I will show you the differences between the disk washer and the cylindrical shell method. Most importantly, you need to know when to use which method in different situations.
In a nutshell, if your solid of revolution looks like a cucumber cut in half (shown in the video), then you use the dish washer method. If your solid of revolution does not look like a cucumber cut in half, then you use the cylindrical shell method. I did two examples in the video with the shape rotated around the y axis and the x axis and then I use the disk was...
published: 02 Aug 2021
Electric Field Due to a Charged Disk, Infinite Sheet of Charge, Parallel Plates - Physics Problems
This physics video tutorial explains how to derive the formula needed to calculate the electric field of a charge disk by establishing an inner and outer radius. You will need to understand a few concepts in calculus specifically integration by u-substitution. This video also shows you how to find the equation to calculate the electric field produced by an infinite sheet of charge using the charge per unit area factor and how to get the electric field between two parallel plates or infinite sheets or plane of charge. This video contains plenty of examples and practice problems.
published: 07 Jan 2017
Electric Field from a Disk
published: 21 Jan 2018
The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. (a) U
The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error in the calculated area of the disk. (b) What is the relative error? What is the percentage error?
This calculus video tutorial explains how to use the disk method and the washer method to calculate the volume of a solid when the region enclosed by the curves...
This calculus video tutorial explains how to use the disk method and the washer method to calculate the volume of a solid when the region enclosed by the curves are rotated around the x axis, y axis, and non axis or another line parallel to the x or y axis. This video contains plenty of examples and practice problems for you to work on. It shows you how to set up and evaluate the definite integral. Techniques include expanding a binomial expression and basic integration rules.
Full 1 Hour 44 Minute Video:
https://www.patreon.com/MathScienceTutor
Direct Link to The Full Video:
https://bit.ly/2V17469
_________________________________
Full 1 Hour 44 Minute Video:
https://www.youtube.com/watch?v=7CMTMCS0Zq0
Join The Membership Program:
https://bit.ly/46xaQTR
This calculus video tutorial explains how to use the disk method and the washer method to calculate the volume of a solid when the region enclosed by the curves are rotated around the x axis, y axis, and non axis or another line parallel to the x or y axis. This video contains plenty of examples and practice problems for you to work on. It shows you how to set up and evaluate the definite integral. Techniques include expanding a binomial expression and basic integration rules.
Full 1 Hour 44 Minute Video:
https://www.patreon.com/MathScienceTutor
Direct Link to The Full Video:
https://bit.ly/2V17469
_________________________________
Full 1 Hour 44 Minute Video:
https://www.youtube.com/watch?v=7CMTMCS0Zq0
Join The Membership Program:
https://bit.ly/46xaQTR
There can not only be just one differential element for a particular uniform rigid body but more.Here we demostrate how to find the area of a disc using differe...
There can not only be just one differential element for a particular uniform rigid body but more.Here we demostrate how to find the area of a disc using differential elements method in 3 different ways using animations
There can not only be just one differential element for a particular uniform rigid body but more.Here we demostrate how to find the area of a disc using differential elements method in 3 different ways using animations
Physics Ninja looks at the problem of calculating the electric field from a ring and disk by integration. The ring and the disk are uniformly charged the fie...
Physics Ninja looks at the problem of calculating the electric field from a ring and disk by integration. The ring and the disk are uniformly charged the field is calculated for a point on the axis.
Physics Ninja looks at the problem of calculating the electric field from a ring and disk by integration. The ring and the disk are uniformly charged the field is calculated for a point on the axis.
There are two ways to find the volume of three dimensional objects in calculus: the disk washer method and the cylindrical shell method.
What is the disk washe...
There are two ways to find the volume of three dimensional objects in calculus: the disk washer method and the cylindrical shell method.
What is the disk washer method? What is the cylindrical shell method? That's exactly what I'm going to talk about today. I will show you the differences between the disk washer and the cylindrical shell method. Most importantly, you need to know when to use which method in different situations.
In a nutshell, if your solid of revolution looks like a cucumber cut in half (shown in the video), then you use the dish washer method. If your solid of revolution does not look like a cucumber cut in half, then you use the cylindrical shell method. I did two examples in the video with the shape rotated around the y axis and the x axis and then I use the disk washer and cylindrical shell method to find the volume.
LIKE & SUBSCRIBE:
🔴 My Channel: www.youtube.com/c/QuocDatPhung
🔴 My second channel: https://www.youtube.com/channel/UCtgROmYhSv97aE11LMiB7yg
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✅Camera: Samsung Galaxy J7
✅Recording Equipment: https://obsproject.com/
✅Editing Software: Shotcut
✅Online Photoshop: https://pixlr.com/e/
There are two ways to find the volume of three dimensional objects in calculus: the disk washer method and the cylindrical shell method.
What is the disk washer method? What is the cylindrical shell method? That's exactly what I'm going to talk about today. I will show you the differences between the disk washer and the cylindrical shell method. Most importantly, you need to know when to use which method in different situations.
In a nutshell, if your solid of revolution looks like a cucumber cut in half (shown in the video), then you use the dish washer method. If your solid of revolution does not look like a cucumber cut in half, then you use the cylindrical shell method. I did two examples in the video with the shape rotated around the y axis and the x axis and then I use the disk washer and cylindrical shell method to find the volume.
LIKE & SUBSCRIBE:
🔴 My Channel: www.youtube.com/c/QuocDatPhung
🔴 My second channel: https://www.youtube.com/channel/UCtgROmYhSv97aE11LMiB7yg
MY EQUIPMENT:
✅Camera: Samsung Galaxy J7
✅Recording Equipment: https://obsproject.com/
✅Editing Software: Shotcut
✅Online Photoshop: https://pixlr.com/e/
This physics video tutorial explains how to derive the formula needed to calculate the electric field of a charge disk by establishing an inner and outer radius...
This physics video tutorial explains how to derive the formula needed to calculate the electric field of a charge disk by establishing an inner and outer radius. You will need to understand a few concepts in calculus specifically integration by u-substitution. This video also shows you how to find the equation to calculate the electric field produced by an infinite sheet of charge using the charge per unit area factor and how to get the electric field between two parallel plates or infinite sheets or plane of charge. This video contains plenty of examples and practice problems.
This physics video tutorial explains how to derive the formula needed to calculate the electric field of a charge disk by establishing an inner and outer radius. You will need to understand a few concepts in calculus specifically integration by u-substitution. This video also shows you how to find the equation to calculate the electric field produced by an infinite sheet of charge using the charge per unit area factor and how to get the electric field between two parallel plates or infinite sheets or plane of charge. This video contains plenty of examples and practice problems.
The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error in the calcul...
The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error in the calculated area of the disk. (b) What is the relative error? What is the percentage error?
The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error in the calculated area of the disk. (b) What is the relative error? What is the percentage error?
This calculus video tutorial explains how to use the disk method and the washer method to calculate the volume of a solid when the region enclosed by the curves are rotated around the x axis, y axis, and non axis or another line parallel to the x or y axis. This video contains plenty of examples and practice problems for you to work on. It shows you how to set up and evaluate the definite integral. Techniques include expanding a binomial expression and basic integration rules.
Full 1 Hour 44 Minute Video:
https://www.patreon.com/MathScienceTutor
Direct Link to The Full Video:
https://bit.ly/2V17469
_________________________________
Full 1 Hour 44 Minute Video:
https://www.youtube.com/watch?v=7CMTMCS0Zq0
Join The Membership Program:
https://bit.ly/46xaQTR
There can not only be just one differential element for a particular uniform rigid body but more.Here we demostrate how to find the area of a disc using differential elements method in 3 different ways using animations
Physics Ninja looks at the problem of calculating the electric field from a ring and disk by integration. The ring and the disk are uniformly charged the field is calculated for a point on the axis.
There are two ways to find the volume of three dimensional objects in calculus: the disk washer method and the cylindrical shell method.
What is the disk washer method? What is the cylindrical shell method? That's exactly what I'm going to talk about today. I will show you the differences between the disk washer and the cylindrical shell method. Most importantly, you need to know when to use which method in different situations.
In a nutshell, if your solid of revolution looks like a cucumber cut in half (shown in the video), then you use the dish washer method. If your solid of revolution does not look like a cucumber cut in half, then you use the cylindrical shell method. I did two examples in the video with the shape rotated around the y axis and the x axis and then I use the disk washer and cylindrical shell method to find the volume.
LIKE & SUBSCRIBE:
🔴 My Channel: www.youtube.com/c/QuocDatPhung
🔴 My second channel: https://www.youtube.com/channel/UCtgROmYhSv97aE11LMiB7yg
MY EQUIPMENT:
✅Camera: Samsung Galaxy J7
✅Recording Equipment: https://obsproject.com/
✅Editing Software: Shotcut
✅Online Photoshop: https://pixlr.com/e/
This physics video tutorial explains how to derive the formula needed to calculate the electric field of a charge disk by establishing an inner and outer radius. You will need to understand a few concepts in calculus specifically integration by u-substitution. This video also shows you how to find the equation to calculate the electric field produced by an infinite sheet of charge using the charge per unit area factor and how to get the electric field between two parallel plates or infinite sheets or plane of charge. This video contains plenty of examples and practice problems.
The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error in the calculated area of the disk. (b) What is the relative error? What is the percentage error?
The area of a disk, more commonly called the area of a circle, of radiusr is equal to πr2. Here the symbol π (Greek letter pi) denotes the constant ratio of the circumference of a circle to its diameter or of the area of a circle to the square of its radius. Since the area of a regular polygon is half its perimeter times its apothem, and a regular polygon approaches a circle as the number of sides increase, the area of a disk is half its circumference times its radius (i.e. 1⁄2 × 2πr × r).
History
Modern mathematics can obtain the area using the methods of integral calculus or its more sophisticated offspring, real analysis. However the area of circles was studied by the Ancient Greeks. Eudoxus of Cnidus in the fifth century B.C. had found that the areas of circles are proportional to their radius squared. The great mathematician Archimedes used the tools of Euclidean geometry to show that the area inside a circle is equal to that of a right triangle whose base has the length of the circle's circumference and whose height equals the circle's radius in his book Measurement of a Circle. The circumference is 2πr, and the area of a triangle is half the base times the height, yielding the area πr2 for the disk. Prior to Archimedes, Hippocrates of Chios was the first to show that the area of a disk is proportional to the square of its diameter, as part of his quadrature of the lune of Hippocrates, but did not identify the constant of proportionality.