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The theorem of Pappus and Guldinus is used to find the ____________
- a)Surface area of the body
- b)Surface area of the body of revolution
- c)Surface area of the body of linear motion
- d)Surface area of the body of rectangular motion
Correct answer is option 'B'. Can you explain this answer?
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The theorem of Pappus and Guldinus is used to find the ____________a)S...
The theorem is used to find the surface area and the volume of the revolving body. This is done by using simple integration. Thus the surface area and the volume of any 2D curve being rotated can be made to be calculated from this theorem.
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The theorem of Pappus and Guldinus is used to find the ____________a)S...
The Pappus-Guldinus theorem is used to determine the surface area and volume of a body of revolution. It is a mathematical formula that relates the surface area and volume of a solid of revolution to the path traced out by the centroid of the shape. This theorem is named after two mathematicians, Pappus of Alexandria and Paul Guldinus.
Body of Revolution
A body of revolution is a three-dimensional shape that is formed by rotating a two-dimensional shape about an axis. Examples of bodies of revolution include spheres, cones, cylinders, and toroids. The surface area and volume of these shapes can be determined using the Pappus-Guldinus theorem.
The Pappus-Guldinus Theorem
The theorem states that the surface area and volume of a body of revolution can be calculated by multiplying the path traced by the centroid by the length of the path. The centroid is the geometric center of the two-dimensional shape that is rotated to form the body of revolution.
The formula for the surface area of a body of revolution is:
A = 2πyA
where A is the area of the two-dimensional shape, y is the distance between the centroid and the axis of rotation, and A is the length of the path traced by the centroid.
The formula for the volume of a body of revolution is:
V = πy^2A
where A is the area of the two-dimensional shape, y is the distance between the centroid and the axis of rotation, and A is the length of the path traced by the centroid.
Conclusion
Therefore, the Pappus-Guldinus theorem is a useful tool for calculating the surface area and volume of bodies of revolution. It is commonly used in engineering and physics to solve problems related to rotating shapes.
Body of Revolution
A body of revolution is a three-dimensional shape that is formed by rotating a two-dimensional shape about an axis. Examples of bodies of revolution include spheres, cones, cylinders, and toroids. The surface area and volume of these shapes can be determined using the Pappus-Guldinus theorem.
The Pappus-Guldinus Theorem
The theorem states that the surface area and volume of a body of revolution can be calculated by multiplying the path traced by the centroid by the length of the path. The centroid is the geometric center of the two-dimensional shape that is rotated to form the body of revolution.
The formula for the surface area of a body of revolution is:
A = 2πyA
where A is the area of the two-dimensional shape, y is the distance between the centroid and the axis of rotation, and A is the length of the path traced by the centroid.
The formula for the volume of a body of revolution is:
V = πy^2A
where A is the area of the two-dimensional shape, y is the distance between the centroid and the axis of rotation, and A is the length of the path traced by the centroid.
Conclusion
Therefore, the Pappus-Guldinus theorem is a useful tool for calculating the surface area and volume of bodies of revolution. It is commonly used in engineering and physics to solve problems related to rotating shapes.
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The theorem of Pappus and Guldinus is used to find the ____________a)Surface area of the bodyb)Surface area of the body of revolutionc)Surface area of the body of linear motiond)Surface area of the body of rectangular motionCorrect answer is option 'B'. Can you explain this answer?
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