
i.5.31 Volume of a solid
condition: Calculate the volume of a body bounded by given surfaces using a triple integral. When calculating the triple integral, go to cylindrical or spherical coordinates. \[ \begin{array}{l} z=2-x^{2}-y^{2}, \quad x^{2}+y^{2}=1, \quad z=0, \\ y=0, \quad(y \geq 0) . \end{array}\]