Open App

Mechanical Engineering Exam > Mechanical Engineering Videos > Theorem 2 : Theorems of Pappus and Guldinus

Theorem 2 : Theorems of Pappus and Guldinus Video Lecture - Mechanical Engineering

FAQs on Theorem 2 : Theorems of Pappus and Guldinus Video Lecture - Mechanical Engineering

1. What are the Theorems of Pappus and Guldinus?

Ans. The Theorems of Pappus and Guldinus are mathematical theorems that relate to the calculation of the volume and surface area of a solid of revolution.

2. How does the Theorem of Pappus help in finding the volume of a solid of revolution?

Ans. The Theorem of Pappus provides a method to find the volume of a solid of revolution by multiplying the area of the shape's cross-section by the distance traveled by the centroid of the shape during the revolution.

3. Can the Theorems of Pappus and Guldinus be applied to any shape?

Ans. The Theorems of Pappus and Guldinus can be applied to any shape that can be generated by rotating a curve around an axis. This includes shapes like spheres, cones, cylinders, and more.

4. How does the Theorem of Guldinus help in finding the surface area of a solid of revolution?

Ans. The Theorem of Guldinus states that the surface area of a solid of revolution is equal to the product of the length of the generating curve and the distance traveled by the centroid of the curve during the revolution.

5. Can the Theorems of Pappus and Guldinus be used in real-life applications?

Ans. Yes, the Theorems of Pappus and Guldinus have various real-life applications. They are commonly used in engineering, physics, and architecture to calculate volumes of objects with rotational symmetry, such as pipes, propellers, and tanks.

Text Transcript from Video

welcome to electron lime here's the
second theorem of pappus guldinus this
case it says that the volume of the body
formed by rotating an area about an axis
is equal to the area multiplied by the
distance covered by the centroid during
the rotation here we have an area here's
the centroid of the area we're going to
rotate that about the x-axis the object
that we end up with will look like this
do it again here so and then here this
of course you can see it's behind and
that would be behind like that all right
and then we should then continue to
rotate this area through then we get
something that looks like this and like
that and I'll not quite what I want it
to look like but I think we have a
pretty good idea if we now raise that
and raise that we now can see that this
is kind of like a a cylinder a hollow
cylinder the distance from the centroid
to the axis of rotation this distance
right here is the y coordinate of the
centroid of the position or the
coordinate of the centroid now what
we're going to do is want to find the
volume of this the volume is equal to
question mark and according to pappus
guldinus theorem it says that the volume
is equal to the area multiplied so we're
going to take the area and we multiply
that times the distance covered by the
centroid the center will travel this
distance Central will go around like
this and then around back like that it
will make a circular path the length of
a circle is 2 pi thon the radius so
multiply this times 2 pi and the radius
in this case will be the y coordinate of
the centroid of that area so we multiply
that times the y coordinate of the
centroid and that is all we need to find
the volume of this hollowed-out cylinder
very very nice technique again we can
use that because the concept of the
centroid and how it affects the
calculation simply the area of the
object right here and 2 pi r which is 2
pi times the y coordinate of the
centroid us who rotate around the x axis
it's all we need to do now we will do
some examples of this so it becomes
clear how nice the taking you get is to
use some cases it may not be easy
because we still need to find the area
which may not be easy to find
but once we have the area we know the
coordinates of the centroid then it's
easy to find the volume of the object
and that's how it's done

About this Video

4.73/5 Rating

Oct 03, 2025 Last updated

Related Exams

Mechanical Engineering Civil Engineering (CE)

Theorem 2 : Theorems of Pappus and Guldinus for Mechanical Engineering2025 is part of Mechanical Engineering preparation. The notes and questions for Theorem 2 : Theorems of Pappus and Guldinus have been prepared according to the Mechanical Engineering exam syllabus. Information about Theorem 2 : Theorems of Pappus and Guldinus covers all important topics for Mechanical Engineering2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Theorem 2 : Theorems of Pappus and Guldinus.

Introduction of Theorem 2 : Theorems of Pappus and Guldinus in English is available as part of our Mechanical Engineering preparation & Theorem 2 : Theorems of Pappus and Guldinus in Hindi for Mechanical Engineering courses. Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.

Description

Video Lecture & Questions for Theorem 2 : Theorems of Pappus and Guldinus Video Lecture - Mechanical Engineering - Mechanical Engineering full syllabus preparation | Free video for Mechanical Engineering exam.

Information about Theorem 2 : Theorems of Pappus and Guldinus

Here you can find the Theorem 2 : Theorems of Pappus and Guldinus defined & explained in the simplest way possible. Besides explaining types of Theorem 2 : Theorems of Pappus and Guldinus theory, EduRev gives you an ample number of questions to practice Theorem 2 : Theorems of Pappus and Guldinus tests, examples and also practice Mechanical Engineering tests.