Non-negative intensity is used to identify the surface areas of a structure that contributes to the scattered sound power. In the acoustic near field, the scattered sound power is predicted using non-negative intensity, as well as the scattered acoustic intensity integrated directly over the scatterer's surface area. In the acoustic far field, the scattered acoustic intensity and the scattered sound power are evaluated for three different receiver surface areas, corresponding to a sphere representing a far-field area that fully circumscribes the scatterer, and two hemispherical surfaces that correspond to partial far-field areas that do not fully circumscribe the scatterer. Back-calculated non-negative intensity that defines the sound scattered from the full or partial far-field receiver surface areas is also calculated and compared to the non-negative intensity obtained directly from the surface of the scatterer. To illustrate the numerical technique, the scattered acoustic intensity and scattered sound power of a rigid sphere, a rigid cylinder, and a rigid hemispherical shell are examined.