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Use the Theorem of Pappus to find the volume of the given solid. the solid obtained by rotating the triangle with vertices (2, 3), (2, 7), and (8, 5) about the x-axis 0

Use the Theorem of Pappus to find the volume of the given solid. the solid obtained by rotating the triangle with vertices (2, 3), (2, 7), and (8, 5) about the x-axis 0

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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**Volume of a Solid Using the Theorem of Pappus** To find the volume of the given solid, use the Theorem of Pappus. The solid is obtained by rotating the triangle with vertices (2, 3), (2, 7), and (8, 5) around the x-axis. **Diagram Explanation:** The diagram shows a three-dimensional view of the solid formed by rotating a triangle around the x-axis. The triangle is highlighted in red with the following vertices: - (2, 3) - (2, 7) - (8, 5) After rotation, the solid appears as a three-dimensional object symmetric about the x-axis, resembling a cylinder with an elliptical cross-section. The rotation creates an ellipsoid shape as the triangle sweeps around the axis. The illustration depicts the y-axis vertically and x-axis horizontally, with the rotation of the triangle forming the solid shown in blue shading. The triangular cross-section is visible where the red triangle was initially before rotation.
Transcribed Image Text:**Volume of a Solid Using the Theorem of Pappus** To find the volume of the given solid, use the Theorem of Pappus. The solid is obtained by rotating the triangle with vertices (2, 3), (2, 7), and (8, 5) around the x-axis. **Diagram Explanation:** The diagram shows a three-dimensional view of the solid formed by rotating a triangle around the x-axis. The triangle is highlighted in red with the following vertices: - (2, 3) - (2, 7) - (8, 5) After rotation, the solid appears as a three-dimensional object symmetric about the x-axis, resembling a cylinder with an elliptical cross-section. The rotation creates an ellipsoid shape as the triangle sweeps around the axis. The illustration depicts the y-axis vertically and x-axis horizontally, with the rotation of the triangle forming the solid shown in blue shading. The triangular cross-section is visible where the red triangle was initially before rotation.
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