The volume of a solid using spherical coordinates

tim@creighton
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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
 
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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
You need to try something before we can provide help.

In your relevant equations, what is this: ρ=x+y+z ?

And this isn't even an equation: dρdφdθ.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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