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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.

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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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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