Let a and c be fixed positive numbers. Consider the two surfaces S₁ z = √² - : 2 (4)² (x² + y²) and S2: z = √x² + y² in R³. Let V be the solid body bounded by the two surfaces, i.e., the finite region above S2 and below S₁ in R³. The boundary surface S of V is the union of S₁ S₂ = S₂ns (where SS is the part of S belonging to S₁ for i = 1, 2). 1. Calculate the volume of V. 2. Calculate the outward pointing unit normal vectors for S₁ and for S2. 3. Calculate the outward flux cross S of the vector field F = −¼¡ = Si n S and У X -i + −j + 22 -k. a c2 a જ

Let a and c be fixed positive numbers. Consider the two surfaces S₁ z = √² - : 2 (4)² (x² + y²) and S2: z = √x² + y² in R³. Let V be the solid body bounded by the two surfaces, i.e., the finite region above S2 and below S₁ in R³. The boundary surface S of V is the union of S₁ S₂ = S₂ns (where SS is the part of S belonging to S₁ for i = 1, 2). 1. Calculate the volume of V. 2. Calculate the outward pointing unit normal vectors for S₁ and for S2. 3. Calculate the outward flux cross S of the vector field F = −¼¡ = Si n S and У X -i + −j + 22 -k. a c2 a જ

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

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