Why does a heap of sand or a hill have a conical shape? 
Sand takes the shape of a cone when it falls on the surface of the earth. Why does sand when poured on the surface of the earth make a conical shape? Why does a heap of sand or a mountain or a hill have a conical shape in terms of the angle of repose?
 A: Imagine each grain of sand as a rock lying on the side of a mountain. There will be a certain 'critical' steepness of the mountain, above which the rock will start to roll.
Now apply this idea to the pile of sand. If the pile is steeper than the critical angle, then grains of sand will roll downhill and pile up at the bottom (i.e. the edge of the pile). This has the effect of reducing the angle of the slope.
Conversely if the slope of the pile is less than the critical angle, then the grains will not roll away so other grains will pile up on top of them. This has the effect of increasing the angle of the slope.
The combination of these two effects means that as more sand is added, the shape of the pile constantly adjusts itself so that the slope in any one place on the surface is about equal to the critical angle. And the only geometric shape that can meet this criterion is a cone.
A: I would give you some intuition behind this. When some sand falls on the ground, the sand is collected on the ground, and the 'heap' begins to rise. Now whatever sand falls, on already collected sand, on boundaries, they begin to fall and roll-off, and so a conical shape is eventually formed. Moreover, the lower portions of the conical heap having a larger cross-section area reduces the pressure of the weight of sand above. So the formation of a roughly conical heap is favorable, or we can say it is easily formed and is a stable structure.
A: Both of the answers supplied so far provide a reason why the pile will be conical in terms of a critical stability angle for sand grains. But there is a little more that should be added.
Firstly, the critical angle will depend to some extent on the properties of the sand grains. Smoothly rounded nearly-spherical grains with a low coefficient of friction will result in a flatter cone than small brick-shaped grains with a high coefficient of friction for example.
Secondly, the conical shape only results when internal stresses/pressures within the pile are small compared with the deformation limits of the grains. So, a sand hill 100 m tall may have a shape almost identical to that of a hill only 1 m tall. But somewhere between the heights of Annapurna and Olympus Mons, the internal stresses will be such that the heap will begin to deform. So for a really tall sand-hill, the lower slopes will be at a shallower angle than the critical angle.
