2. Let a and c be fixed positive numbers. Consider the two surfaces 155 : 2 = c2 (4)² (x² + y²) and S₂ z = √x² + y² : = Si n S and 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 S2S2S (where SnS 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 = a -Mi+j+20k −j+ 22 k. α

2. Let a and c be fixed positive numbers. Consider the two surfaces 155 : 2 = c2 (4)² (x² + y²) and S₂ z = √x² + y² : = Si n S and 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 S2S2S (where SnS 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 = a -Mi+j+20k −j+ 22 k. α

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 33E

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