I.5.31 Volume of a Solid

Condition: calculate the volume of the body limited by the specified 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} \]