Integrate[Integrate[Integrate[1,{z,(Sqrt[(x^2)+(y^2)]),(Sqrt[1-(x^2)-(y^2)])}],{y,-(Sqrt[(1/2)-(x^2)]),(Sqrt[(1/2)-(x^2)])}],{x,-(1/(Sqrt[2])),(1/(Sqrt[2]))}]

FullSimplify[Integrate[Integrate[Integrate[1 r,{z,r,(Sqrt[1-(r^2)])}],{r,0,(Sqrt[(1/2)])}],{θ,0,2 Pi}]]

FullSimplify[Integrate[Integrate[Integrate[1 (ρ^2)Sin[ϕ],{ϕ,0,(π/4)}],{ρ,0,1}],{θ,0,2 Pi}]]

FullSimplify[Integrate[Integrate[Integrate[ρ Sin[ϕ] (ρ^2)Sin[ϕ],{ϕ,0,π}],{ρ,1,2}],{θ,0,2 Pi}]]

(((15 (π^2))/4)/((28 π)/3))

N[%]

ParametricPlot[{Cos[5t], Sin[2t]},{t,0,2 Pi},ImageSize->250]

ParametricPlot3D[{t Cos[t], t Sin[t],t},{t,0,16 Pi},ImageSize->250,BoxRatios->{1,1,1}]