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36 – x² – y² and S2 be the Let Si be the hemisphere with Cartesian equation z = 6 – upper nappe of the cone x² + y² – 3z2 = 0. %3D a. The curve of intersection of S1 and S2 is a circle. Find the radius and the coordinates of the center of this circle. b. Find an equation in spherical coordinates for S1. c. Let G2 the solid enclosed by S1 and S2. a. Set up an iterated triple integral in cylindrical coordinates that yields the volume of G2. Do not evaluate the integral. b. Find the volume of G2 using a triple integral in spherical coordinates.

36 – x² – y² and S2 be the Let Si be the hemisphere with Cartesian equation z = 6 – upper nappe of the cone x² + y² – 3z2 = 0. %3D a. The curve of intersection of S1 and S2 is a circle. Find the radius and the coordinates of the center of this circle. b. Find an equation in spherical coordinates for S1. c. Let G2 the solid enclosed by S1 and S2. a. Set up an iterated triple integral in cylindrical coordinates that yields the volume of G2. Do not evaluate the integral. b. Find the volume of G2 using a triple integral in spherical coordinates.

Advanced Engineering Mathematics
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 answer c: a and b.

Let Si be the hemisphere with Cartesian equation z = 6 – V36 – x² – y² and S2 be the upper nappe of the cone x² + y? – 3z2 = 0. a. The curve of intersection of S1 and S2 is a circle. Find the radius and the coordinates of the center of this circle. b. Find an equation in spherical coordinates for S1. c. Let G2 the solid enclosed by S1 and S2. a. Set up an iterated triple integral in cylindrical coordinates that yields the volume of G2. Do not evaluate the integral. b. Find the volume of G2 using a triple integral in spherical coordinates.
Transcribed Image Text:Let Si be the hemisphere with Cartesian equation z = 6 – V36 – x² – y² and S2 be the upper nappe of the cone x² + y? – 3z2 = 0. a. The curve of intersection of S1 and S2 is a circle. Find the radius and the coordinates of the center of this circle. b. Find an equation in spherical coordinates for S1. c. Let G2 the solid enclosed by S1 and S2. a. Set up an iterated triple integral in cylindrical coordinates that yields the volume of G2. Do not evaluate the integral. b. Find the volume of G2 using a triple integral in spherical coordinates.
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