Find Pappus's Theorem for Volume in your text. It turns out, he went farther than that (still without calculus) and also found a formula for Surface Area which is S = 27pL where p is distance from the axis of revolution to the centroid and L is the length of the arc times the distance traveled by the arc's centroid during the revolution. Demonstrating the use of these theorems find the volume and the surface area of the torus found by revolving a circular disk of radius a about an axis in the its plane at a distance b≥ a from its center. (Include your best labeled picture here.)
Find Pappus's Theorem for Volume in your text. It turns out, he went farther than that (still without calculus) and also found a formula for Surface Area which is S = 27pL where p is distance from the axis of revolution to the centroid and L is the length of the arc times the distance traveled by the arc's centroid during the revolution. Demonstrating the use of these theorems find the volume and the surface area of the torus found by revolving a circular disk of radius a about an axis in the its plane at a distance b≥ a from its center. (Include your best labeled picture here.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Find Pappus's Theorem for Volume in your text. It turns out, he went farther than that (still without calculus) and also found a formula for Surface Area which is \( S = 2\pi \rho L \) where \( \rho \) is distance from the axis of revolution to the centroid and \( L \) is the length of the arc times the distance traveled by the arc’s centroid during the revolution. Demonstrating the use of these theorems find the volume and the surface area of the torus found by revolving a circular disk of radius \( a \) about an axis in the its plane at a distance \( b \geq a \) from its center. (Include your best labeled picture here.)
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Step 1
The volume of a solid of revolution generated by the revolution of a lamina about an external axis is equal to , d2 is the distance traveled by the lamina's geometric centroid about the axis of revolution.
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