3. The region R is bounded by y = √9-x² and y = 0. • Revolving R about the x-axis produces a solid S₁. • R is also the base of a solid S₂. Cross-sections through S₂ taken parallel to the x-axis are semicircles. Let V₁ be the volume of S₁ and let V₂ be the volume of S₂. Use geometric reasoning (not computations) to find a constant a so V₁ = a · V₂ and explain your answer using words and pictures.
3. The region R is bounded by y = √9-x² and y = 0. • Revolving R about the x-axis produces a solid S₁. • R is also the base of a solid S₂. Cross-sections through S₂ taken parallel to the x-axis are semicircles. Let V₁ be the volume of S₁ and let V₂ be the volume of S₂. Use geometric reasoning (not computations) to find a constant a so V₁ = a · V₂ and explain your answer using words and pictures.
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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Please show all work with pictures please, thank you
Transcribed Image Text:3.
The region R is bounded by y = √9-x² and y = 0.
• Revolving R about the x-axis produces a solid S₁.
• R is also the base of a solid S₂. Cross-sections through S₂ taken parallel to the x-axis are semicircles.
Let V₁ be the volume of S₁ and let V₂ be the volume of S₂. Use geometric reasoning (not computations) to find a constant
a so V₁ = a · V₂ and explain your answer using words and pictures.
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