The area of a hemisphere for a ‘point’ source on the ground is given by 2πr2, where r is the distance from the source in metres. However, if the source is not a single point, the area of the surrounding surface a given distance from it depends upon the dimensions of the source. For example, for a cuboid source on the ground 3m long x 2m wide x 1.5m high, the area of the surface 1m from the source will be a larger cuboid of 5m long x 4m wide x 2.5m high (2m longer and wider but 1m taller than the source). This has an area of 65m2.
Moving to 2m from the source increases the surrounding surface to 7m x 6m x 3.5m with an area of 133m2. Unlike a point source, the surface area does not quadruple with every doubling of distance for larger sources, although at greater distances the size of the source gradually becomes insignificant. In this case the area only approximately doubles, giving a 3dB reduction with doubling of distance rather than 6dB (because this is in the ‘near field’ rather than ‘far field’).
As a rule of thumb, there is negligible change in sound level with distance from a source when within approximately one third of the smaller source face dimension. The sound level then reduces at a rate of approximately 3dB per doubling of distance up to approximately one third of the larger source face dimension. Then the sound level starts reducing at a rate of approximately 6dB per doubling of distance from the source.