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A region bounded by f(x) = 5 - x, y = 1, and x = 1 is shown. What is the volume of the solid formed by revolving the region about the x-axis? 765 4 3 -2-11 1 2 3 4 5 6 7 8 ○18 ○9 c0100 이상 16 ㅠ 음ㅠ

A region bounded by f(x) = 5 - x, y = 1, and x = 1 is shown. What is the volume of the solid formed by revolving the region about the x-axis? 765 4 3 -2-11 1 2 3 4 5 6 7 8 ○18 ○9 c0100 이상 16 ㅠ 음ㅠ

Calculus: Early Transcendentals
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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### Volume of Solid of Revolution **Problem Statement:** A region bounded by \( f(x) = 5 - x \), \( y = 1 \), and \( x = 1 \) is shown. What is the volume of the solid formed by revolving the region about the x-axis? **Graph Explanation:** The graph shows the region bounded by the line \( f(x) = 5 - x \), the line \( y = 1 \), and the vertical line \( x = 1 \). Here is a more detailed description: - The function \( f(x) = 5 - x \) is a straight line with a negative slope, moving downward from the y-intercept at \( (0, 5) \) to the x-intercept at \( (5, 0) \). - The horizontal line \( y = 1 \) intersects the y-axis at (0, 1) and extends to the right. - The vertical line \( x = 1 \) is parallel to the y-axis and intersects the x-axis at \( x = 1 \). The shaded region is the area bounded by these lines. The region is then revolved around the x-axis to create a solid of revolution. **Possible Answers:** - \( \boxed{18\pi} \) - \( \boxed{9\pi} \) - \( \boxed{\frac{16}{3}\pi} \) - \( \boxed{\frac{8}{3}\pi} \)
Transcribed Image Text:### Volume of Solid of Revolution **Problem Statement:** A region bounded by \( f(x) = 5 - x \), \( y = 1 \), and \( x = 1 \) is shown. What is the volume of the solid formed by revolving the region about the x-axis? **Graph Explanation:** The graph shows the region bounded by the line \( f(x) = 5 - x \), the line \( y = 1 \), and the vertical line \( x = 1 \). Here is a more detailed description: - The function \( f(x) = 5 - x \) is a straight line with a negative slope, moving downward from the y-intercept at \( (0, 5) \) to the x-intercept at \( (5, 0) \). - The horizontal line \( y = 1 \) intersects the y-axis at (0, 1) and extends to the right. - The vertical line \( x = 1 \) is parallel to the y-axis and intersects the x-axis at \( x = 1 \). The shaded region is the area bounded by these lines. The region is then revolved around the x-axis to create a solid of revolution. **Possible Answers:** - \( \boxed{18\pi} \) - \( \boxed{9\pi} \) - \( \boxed{\frac{16}{3}\pi} \) - \( \boxed{\frac{8}{3}\pi} \)
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