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.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.3: Using Data Displays
Problem 2C
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ad1d6ae-9b72-4395-9138-1384474b8f3a%2Ff40d493b-d00f-41bb-b88e-c9c823317efb%2F286s0p_processed.png&w=3840&q=75)
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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