Cones on a pointing out from a cylinder I am very new to Blender to please excuse me if I might use the wrong terminology.  

I would like to coat part of a sphere will well packed cones. With this I mean that the cones will have two radii, one connected to the outside of the sphere (let us call it r1), and one sticking out (r2) of the sphere, similarly to what is shown in the image below.  



One approach has been to simply make the cones by hand and try to match the radius of curvature of the sphere with that of the cylinders, however, this has not turned out great because:

1) I have not found a good way to match the radius of curvature of the sphere with r1 and r2.

2) I have not found a good way to snap the sides of the cones without deforming them. I want to snap them while only rotating the snap element (or target).

3) Doing this for many many cones would be very tedious. 

Another approach I have tried was to make an array of several cylinders (r1=r2, same top and bottom radii). I then used a sphere as curve modifier to get a curvature. This worked quite excellently, for one radius. As seen below, the top radius (r2) will be kept intact whereas the bottom radius (r1) is deformed into a oval shape.



So the main issue here was:

1) to keep the bottom area as a circle, and not deformed into an oval. 

2) Also for this approach it would be handy to be able to snap the arrays together

A third approach was quickly tried, which involved duplicating a cylinder on all the faces of the sphere, resulting in the rendition below



The problem here is that the cylinders are of different size but internally have the same top and bottom radius, so this was not the best approach.

Do you have any advice on how to solve this? I am open to all kind of solutions, as there are probably a million ways to actually do this, with more of less finesse.. And I apologise if this is way to basic or if my problem is not very well described. 

All the best

Glassmacka
Here's my attempt:
Use a particle hair system, using a vertex group for density, growing from the vertices of the sphere (or faces, adapt to taste).
Muck about with the scale of the end caps of the cylinder, and the number of segments of the sphere for you needs...
Anything like what you're after?

Can't work out how to throw the blend file on here so-

https://www.dropbox.com/s/z8hpfk6rpbjpvbs/SphereWithConicalHair.blend?dl=0

Cheers
Mark