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
Related questions
Question
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc77acd82-6ee8-4fa1-94f2-256b23fe8b4f%2F33cee5b4-dc6b-42ee-bebe-5dd5ee828a22%2Ff7qfgbq_processed.png&w=3840&q=75)
Transcribed Image Text: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
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