Question 1
Use spherical coordinates [ R, φ, θ] to describe the region enclosed by the half-cone z =

and the sphere x
2 + y
2 + z
2 = 4.
◦ 0 ≤ R ≤ 2, 0 ≤ φ ≤

, 0 ≤ θ ≤ 2π
◦ 0 ≤ R ≤ 2, 0 ≤ φ ≤ π, 0 ≤ θ ≤ 2π
◦ 0 ≤ R ≤ 2, 0 ≤ φ ≤

, 0 ≤ θ ≤ 2π
◦ -2 ≤ R ≤ 2, 0 ≤ φ ≤

, 0 ≤ θ ≤ 2π
◦ -2 ≤ R ≤ 2, -

≤ φ ≤

, 0 ≤ θ ≤ 2π
Question 2
Find the equation of the cone z =

expressed in spherical coordinates [ R, φ, θ].
◦ R =

◦ φ =

◦ R =

◦ φ =

◦ θ =