1. The problem statement, all variables and given/known data The problem and its solution are attached as TheProblemAndSolution.jpg. 2. Relevant equations V(D) = ∫∫∫_D ρ^2 sinθ dρ dϕ dθ 3. The attempt at a solution How exactly does the solution get cos α = 1/√(3)? Also, when the solution goes from the step with two integrals to the step with one integral, is a minus sign forgotten by the author of the solution (because it seems to me that it should be cos(π/2) - cos α, where cos(π/2) = 0)? Also, to be pedantic, given the way the problem is approached in the solution, shouldn't the solution say "in spherical coordinates (ρ, ϕ, θ)" (instead of (ϕ, θ, ρ))?