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## Homework Statement

Describe using spherical coordinates the solid E in the

**first octant**that lies above the half-cone z=√(x

^{2}+y

^{2}) but inside x

^{2}+y

^{2}+z

^{2}=1. Your final answer must be written in set-builder notation.

## Homework Equations

ρ = x

^{2}+y

^{2}+z

^{2}

x = ρsinφcosθ

y = ρsinφsinθ

z = ρcosφ

## The Attempt at a Solution

Since we are in the first octant, θ will go from [0,π/2].

However the problem comes with describing ρ and φ,

Since we are in the first octant I believe that φ will be the same as θ, however for ρ,

I substituted in the relevant equations into both equations that were given.

ρ= ±1 <-- Unit sphere

ρ=√(2ρ

^{2}sin

^{2}φ)/cosφ <-- Half cone

Would I be able to use the positive bound of the unit sphere as the upper limit and the bound gotten from the cone as the lower limit?

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