I don`t understand how to do this question
A solid lies above the cone z = √ x² + y² and outside the sphere x² + y² + z² = 4z. Write a description of the solid in terms of inequalities involving spherical coordinates.
A solid lies above the cone z = √ x² + y² and outside the sphere x² + y² + z² = 4z. Write a description of the solid in terms of inequalities involving spherical coordinates.
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In spherical coordinates,
z = √(x² + y²) ==> ρ cos φ = ρ sin φ ==> φ = π/4
x² + y² + z² = 4z ==> ρ² = 4ρ cos φ ==> ρ = 4 cos φ.
So, we have 0 ≤ ρ ≤ 4 cos φ, 0 ≤ φ ≤ π/4, and 0 ≤ θ ≤ 2π.
I hope this helps!
z = √(x² + y²) ==> ρ cos φ = ρ sin φ ==> φ = π/4
x² + y² + z² = 4z ==> ρ² = 4ρ cos φ ==> ρ = 4 cos φ.
So, we have 0 ≤ ρ ≤ 4 cos φ, 0 ≤ φ ≤ π/4, and 0 ≤ θ ≤ 2π.
I hope this helps!