Video Example EXAMPLE 2 Find the volume of the solid bounded by the plane z = 0 and the paraboloid z = 1 - x2 - y2. SOLUTION If we put z = 0 in the equation of the paraboloid, we get x2 + y2 = 1, so the solid lies under the paraboloid and above the circular disk D given by x2 + y2 ≤ 1. In polar coordinates D is given by 0 ≤ r ≤ 1, 0 ≤ θ ≤ 2π. Since 1 - x2 - y2 = 1 - r2, the volume is V = int int (1 - x2 - y2)dA = int_0^(2pi) int_0^1 (1 - r2)r dr dθ = int_0^(2pi) dθ int_0^1 (1r - r3)dr = 2π [ [_0^1 =