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Find the volume of the solid bounded above by the graph of x2 + y2 +z2 = 5 and below by the graph of x2 +y? = 4z.

Find the volume of the solid bounded above by the graph of x2 + y2 +z2 = 5 and below by the graph of x2 +y? = 4z.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...
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a,d,e,f. please!!

28 The following problems are to be done with triple integrals. You may use cylindrical or spherical coordinates if you wish. Find the volume of the solid bounded above by the graph of x² + y? +z? = 5 and below by the graph of x2 + y? = 4z. b Find the volume of the solid bounded by the graphs of x² + y² + z² = a², +y?% (tan²a)2, with z 2 0, and x? + y? =(tan?pz?, with z 2 0. Here a >0 and 0<B<. c. Find the volume of the smaller solid bounded by two concentric spheres of radii a and b and a plane that passes at a distance e from their centers. Here 0 <c<b<a. Find the volume of the solid lying above the graph of z? = x2 +y? and inside the graph of x? +y2 +z² = 4z. | Find the volume of the solid which lies above the graph of 3z2 = x2 +y2 and %3! inside the graph of x² +y² +z? = 4z. f The smaller solid bounded by the graphs of x2 + y +z? = a? and z = b, with 0 <b< a, has mass density at each point inversely proportional to the square of the distance from that point to the origin. Find its mass.
Transcribed Image Text:28 The following problems are to be done with triple integrals. You may use cylindrical or spherical coordinates if you wish. Find the volume of the solid bounded above by the graph of x² + y? +z? = 5 and below by the graph of x2 + y? = 4z. b Find the volume of the solid bounded by the graphs of x² + y² + z² = a², +y?% (tan²a)2, with z 2 0, and x? + y? =(tan?pz?, with z 2 0. Here a >0 and 0<B<. c. Find the volume of the smaller solid bounded by two concentric spheres of radii a and b and a plane that passes at a distance e from their centers. Here 0 <c<b<a. Find the volume of the solid lying above the graph of z? = x2 +y? and inside the graph of x? +y2 +z² = 4z. | Find the volume of the solid which lies above the graph of 3z2 = x2 +y2 and %3! inside the graph of x² +y² +z? = 4z. f The smaller solid bounded by the graphs of x2 + y +z? = a? and z = b, with 0 <b< a, has mass density at each point inversely proportional to the square of the distance from that point to the origin. Find its mass.
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