Use spherical coordinates to find the smaller volume cut out from the sphere 𝑥^2+𝑦^2+𝑧2=4by the plane z= 1.

Question

Did I set up the limit and integration correctly [0,2π]∫() [0,2π]∫() [sec(𝜑),2]∫()p^2 sin(𝜑)d𝜌𝑑𝜑𝑑𝜃 ?

Answer 1

Use spherical coordinates to find the smaller volume cut out from the sphere 𝑥^2 +𝑦^2 +𝑧^2= 4by the plane z= 1.

Answer 2

since the plane intersects the sphere when θ = π/3 that would make the integral
∫[0,2π]∫[0,π/3]∫[0,2] r^2 sinθ dr dθ dφ

google can provide other examples and videos

Answer 3

Can you explain how you got θ = π/3? The only part I don't get it.