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1. Use Pappus' Theorem to find the volume V of the torus generated by revolving a circular region of radius b about a line at a distance a (greater than b) from center of the circle.

1. Use Pappus' Theorem to find the volume V of the torus generated by revolving a circular region of radius b about a line at a distance a (greater than b) from center of the circle.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Content Bb PowerPoint Presentation A learn-ap-southeast-1-prod-fleet02-xythos.content.blackboardcdn.com/5be3c7fe2b7fc/19813877?X-Blackboard-Expiration=1649062800000&X-Blackboard-Si. A ☆ Classroom M Gmail PowerPoint Presentation 13 / 14 100% + Example: 1. Use Pappus' Theorem to find the volume V of the torus generated by revolving a circular region of radius b about a line at a distance a (greater than b) from center of the circle. Solution: By symmetry, the centroid of the circular region is its center. Thus, Distance traveled by the centroid = 2na Area of the circle with radius b = rb² From Pappus' Theorem, the volume of the torus is V = A·d V= (πb2) (2πα) V=2π αb 2 The centroid travels a distance 2ra. G 4) 1108 AM
Transcribed Image Text:Content Bb PowerPoint Presentation A learn-ap-southeast-1-prod-fleet02-xythos.content.blackboardcdn.com/5be3c7fe2b7fc/19813877?X-Blackboard-Expiration=1649062800000&X-Blackboard-Si. A ☆ Classroom M Gmail PowerPoint Presentation 13 / 14 100% + Example: 1. Use Pappus' Theorem to find the volume V of the torus generated by revolving a circular region of radius b about a line at a distance a (greater than b) from center of the circle. Solution: By symmetry, the centroid of the circular region is its center. Thus, Distance traveled by the centroid = 2na Area of the circle with radius b = rb² From Pappus' Theorem, the volume of the torus is V = A·d V= (πb2) (2πα) V=2π αb 2 The centroid travels a distance 2ra. G 4) 1108 AM
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