Consider the solid inside the sphere x2 + y² + z² = 4, below the cone z = %3D Vx² + y² _and in the first octant. a) Sketch the solid and its projections b) Convert all equations to spherical coordinates and simplify, c) Use spherical coordinates to set up a triple integral that expresses the volume of the solid. Recall that x = p cos o cos 0, y = p sin ø sin 0, z = p cos 4, dV = p²dpdød@.
Consider the solid inside the sphere x2 + y² + z² = 4, below the cone z = %3D Vx² + y² _and in the first octant. a) Sketch the solid and its projections b) Convert all equations to spherical coordinates and simplify, c) Use spherical coordinates to set up a triple integral that expresses the volume of the solid. Recall that x = p cos o cos 0, y = p sin ø sin 0, z = p cos 4, dV = p²dpdød@.
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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Transcribed Image Text:Consider the solid inside the sphere x? + y² + z² = 4, below the cone z =
%3D
|x² + y² _and in the first octant.
a) Sketch the solid and its projections
b) Convert all equations to spherical coordinates and simplify,
c) Use spherical coordinates to set up a triple integral that expresses the volume of the
solid. Recall that x = p cos o cos 0, y = p sin ø sin 0, z = p cos ø, dV =
p²dpdød@.
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