Question 2. Let E be the solid region inside the surface x² + y² + z² = 25 and above the surface z = √3x² + 3y². (a) Sketch the solid region E. (b) Sketch the cross section of E in the yz-plane (when x=0). Shade the region. (c) Sketch the projection of the solid onto the xy-plane. Shade the region. (d) SET UP but do not evaluate the integral in cylindrical coordinates (dz dr de) that gives the volume of E. Indicate how you found the limits of integration for z, r, and 0. (e) SET UP but do not evaluate the integral in spherical coordinates (dp do do) that gives the volume of E. Indicate how you found the limits of integration for p, , and 0. a)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter11: Topics From Analytic Geometry
Section11.2: Ellipses
Problem 63E
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Question 2. Let E be the solid region inside the surface
x² + y² + z² = 25 and above the surface z = √3x² + 3y².
(a) Sketch the solid region E.
(b) Sketch the cross section of E in the yz-plane (when x=0).
Shade the region.
(c) Sketch the projection of the solid onto the xy-plane. Shade the
region.
(d) SET UP but do not evaluate the integral in cylindrical
coordinates (dz dr de) that gives the volume of E. Indicate how
you found the limits of integration for z, r, and 0.
(e) SET UP but do not evaluate the integral in spherical
coordinates (dp do do) that gives the volume of E. Indicate how
you found the limits of integration for p, , and 0.
2
Transcribed Image Text:Question 2. Let E be the solid region inside the surface x² + y² + z² = 25 and above the surface z = √3x² + 3y². (a) Sketch the solid region E. (b) Sketch the cross section of E in the yz-plane (when x=0). Shade the region. (c) Sketch the projection of the solid onto the xy-plane. Shade the region. (d) SET UP but do not evaluate the integral in cylindrical coordinates (dz dr de) that gives the volume of E. Indicate how you found the limits of integration for z, r, and 0. (e) SET UP but do not evaluate the integral in spherical coordinates (dp do do) that gives the volume of E. Indicate how you found the limits of integration for p, , and 0. 2
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