The discussion focuses on calculating the volume of a solid defined by spherical coordinates, specifically the region outside the cone defined by the equation z² = x² + y² and inside the sphere defined by x² + y² + z² = 2. Participants highlight the need for clarity in the equations used, particularly the incorrect representation of ρ as x + y + z, which should instead relate to spherical coordinates. The correct approach involves using the spherical coordinate transformations and integrating over the appropriate bounds to find the volume.
PREREQUISITESStudents studying multivariable calculus, educators teaching spherical coordinates, and anyone interested in solid geometry and volume calculations.
You need to try something before we can provide help.tim@creighton said:Homework Statement
using spherical coordinates find the volume of the solid outside the cone z^2=x^2+y^2 and inside the sphere x^2+y^2+z^2=2
Homework Equations
ρ=x+y+z ρ^2=x^2+y^2+z^2
dρdφdθ
The Attempt at a Solution
im lost