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.)

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

ChapterP: Prologue: Calculator Arithmetic

Section: Chapter Questions

Problem 18E: When the Radius Increases a. A rope is wrapped tightly around a wheel with radius of 2 feet. If the...

See similar textbooks

Similar questions

The radius length of the base of a right circular cylinder is 6 in. The height of the cylinder is 10 in. Find the exact a Lateral area b total area c volume.
Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. A solid right cylinder 9.55 centimeters high contains 1910 cubic centimeters of material. Compute the cross-sectional area of the cylinder.
Cycling The Campagnolo Hyperon Ultra Two carbon wheel, which has a diameter of 700 millimeters, has 22 spokes evenly distributed around the rim of the wheel. What is the length of the rim subtended by adjacent pairs of spokes (Figure 15)?
When the Radius Increases a. A rope is wrapped tightly around a wheel with radius of 2 feet. If the radius of the wheel is increased by 1 foot to a radius 3 feet, by how much must the rope be lengthened to fit around the wheel? b. Consider a rope wrapped around the Earths equator. We noted in Exercise 17 that the radius of the Earth is about 4000 miles. That is 21,120,000 feet. Suppose now that rope is to be suspended exactly 1 foot above the equator. By how much must the rope be lengthened to accomplish this? The Size of the Earth The radius of the Earth is approximately 4000 miles. a. How far is it around the equator? Hint: You are looking for the circumference of a circle b. What is the volume of the Earth? Hint: The volume of a sphere of radius r is given by 43r3. b. What is the surface area of the Earth? Hint: The surface area of a sphere of radius r is given by 4r2.
The tin can shown at the right has the indicated dimensions. Estimate the number of square inches of tin required for its construction. HINT: Include the lid and the base in the result.
Determine whether the statement is true or false. a A right circular cone has exactly two bases. b The lateral area L of a right circular cylinder with radius length r and height h is given by L=2rh.