This seems trivial if you understand triple integration and simple coordinate systems; however, a question of this type made me think for a moment since its not as simple as converting from cylindrical to spherical coordinates or setting up bounds (Ρ, Φ , θ). The solution isn’t as complex as you would imagine. Similar to many other problems, seeing the solution will make you say, “ahh okay.” Lets see what we are tackling.
We have a sphere with radius sqrt(2):
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