From the BBC's Russia: Eight missing in flooded diamond mine:
Many kimberlite and lamproite deposits occur as:
carrot-shaped, vertical intrusions termed 'pipes'
As the term "carrot-shaped" suggests, the general shape of the pipes is conical and when viewed in horizontal cross-sections they are generally quasi-circular.
When such structures are mined by open cut methods, as with open cut mines of tabular orebodies it is impossible to mine any open pit to any great depth with vertical walls for ground stability reasons. The mine walls are stepped and the parts of the walls between the horizontal steps are sloped. Because of this, open pit mines start out wide at the top, on the surface, and they get narrower with depth.
If the deposit being mined has a quasi-circular horizontal cross-section and is shaped something like a carrot then the open cut mine will also be conical or quasi-conical in shape.