Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN: 9781133382119
Author: Swokowski
Publisher: Cengage
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Question
**Educational Transcription: Calculating the Volume of a Solid of Revolution** **Problem Statement:** Find the volume of the solid generated by revolving the shaded region about the given axis. **Details:** - **Equation:** \( x = \frac{y^2}{5} \) - **Axis of Revolution:** About the y-axis **Graph Description:** - The graph displays a shaded region bounded by the curve \( x = \frac{y^2}{5} \), the y-axis, and horizontal lines at \( y = 1 \) and \( y = 6 \). - The region is a section of the xy-plane that resembles a parabolic shape extending from \( y = 1 \) to \( y = 6 \). **Volume Calculation Options:** 1. \( \frac{625}{6} \pi \) 2. \( 25\pi \) 3. \( \frac{250}{3} \pi \) 4. \( 100\pi \) **Instructions:** - Click "Save and Submit" to save and submit your answer. - Click "Save All Answers" to save all your answers. For an educational context, remember to understand the process of revolving a region to find the volume, using integration techniques such as the disk or washer methods, especially when dealing with functions in terms of \( y \).
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Transcribed Image Text:**Educational Transcription: Calculating the Volume of a Solid of Revolution** **Problem Statement:** Find the volume of the solid generated by revolving the shaded region about the given axis. **Details:** - **Equation:** \( x = \frac{y^2}{5} \) - **Axis of Revolution:** About the y-axis **Graph Description:** - The graph displays a shaded region bounded by the curve \( x = \frac{y^2}{5} \), the y-axis, and horizontal lines at \( y = 1 \) and \( y = 6 \). - The region is a section of the xy-plane that resembles a parabolic shape extending from \( y = 1 \) to \( y = 6 \). **Volume Calculation Options:** 1. \( \frac{625}{6} \pi \) 2. \( 25\pi \) 3. \( \frac{250}{3} \pi \) 4. \( 100\pi \) **Instructions:** - Click "Save and Submit" to save and submit your answer. - Click "Save All Answers" to save all your answers. For an educational context, remember to understand the process of revolving a region to find the volume, using integration techniques such as the disk or washer methods, especially when dealing with functions in terms of \( y \).
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