Does it even exist....just a plain ole ordinary ball in 10 mm ?
I have found plenty of flat.

Looking to buy my first 10 in 1911 platform

I have never seen any ball FMJ bullets for 10mm, the constrain is that the radius of the bullet would be too small at the proper COL and not being crimp able! 
The 10mm cartridge has an COL of 1.25" - 1.26" with most bullets as designed.  There are a few that are crimped shorter such as WFN types to help with magazine fit, feeding as it relates to tipping angle.

Cartridge case length of the 10mm  0.990" - 0.987" this doesn't leave much for the bullet to stick out @ 1.26" - 0.988" = 0.272" Max bullet protrusion. 
Whereas 45ACP case length 0.8930" with a COL of 1.27" with Ball ammo...

They arent common. But there are several companies making round nose bullets to reload with.

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If you hand load you can get round nose coated bullets but I've never seen 10mm round nose FMJ loaded ammo. I have Missouri Round Nose 180gr coated bullets that I use for plinkers. They're relatively cheap and don't leave a mess when loading them or in the gun afterwards. Not much help though if you don't handload.

If they are a true round nose the radius will have to be very short.  Most I have seen as round nose still have a flat section on the nose area...

Here's Acmes version of a round nose 40 caliber bullet in a 155 gr bullet. Looks more like a ball with supports on the side. I've also loaded some of the Acme bullets in their coated and non-coated bullets. Their 30-30m 135gr lead is a favorite for plinking or a light load. My nephews love to hunt rabbits with the 30-30s using this bullet and a light load of IMR3031. Almost no recoil.
http://www.acmebullet.com/bullets-reloading-brass/40-10MM-Lead-Hard-Cast-Bullets?product_id=511

Just a point of clarification..."ball" ammo is any full metal jacket ammo.  Most often in 45 acp it was a round nose profile, but flat nose and truncated cone also meet the definition.

Quote from: sqlbullet on December 27 2018 03:55:43 PM MST
Just a point of clarification..."ball" ammo is any full metal jacket ammo.  Most often in 45 acp it was a round nose profile, but flat nose and truncated cone also meet the definition.

My thoughts exactly..

OK to term it correctly FMJRN.
I have been shooting for 30 years now and have found that some-not all semi-auto's do not like flat nose,even though most self defense ammo is kinda flat nosed anyway.
I am looking at 1911 platform for 10mm, specifically a RIA, maybe a couple other manufactures just as long as they are not polymer , really into steel or "metal" hand guns.
I have never had a 10mm cartridge in my hand and I am not a re loader. I know it seems odd that a long time shooter does not load their own but I started collecting ammo years ago when it was really cheap and have a nice little stash. Since everything has gotten way more costly I buy my food for my toys from a local to me family owned business that has super reasonable prices for new and 1 time fired, however they do not do 10mm....until I whine enough 
From statements above it seems a empty 10 cartridge must a long one hence the need for flat nose...am I correct on this assumption ?
I want a 10mm and dont want a flat nose feed issue to be a detourant to my purchase, I would guess the manufactures have surely address any issues with adjusting angles of  feed ramps and mag followers.
There is a show today and the Ma & Pa I frequent has a RIA 10mm 1911-A1  that I am going to go play touchy feely with.
I will also get a chance to "visit" with the ammo dude and do a little 10mm smooching 

Thanks to everybody for clarification and advise, nice forum.

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I would generally say yes, all my 10mm handguns hand a TC or HP profile just fine.  And you can find round nose easy enough, but it is usually cast bullets.  RN-FMJ is indeed not the norm.

All my 1911 10mm's (Ruger, RIA HC, Para HC) are fussy about COAL.  Anything over 1.250" COAL becomes pretty iffy.  But below that they run just fine.

So to sum it up, the purpose of flat point FMJ ammo in 10mm is to avoid feeding issues, not cause them. Looking for someone to load round nose FMJ ammo for you may have the opposite effect FWIW, I can run 1.255 COAL in my Colt and Kimber with no problems. The RIA you're considering should be fine with any ammo at 1.250".

Let us know if you buy it and how you like it after you shoot it.

My suggestion is to try any of a number of the standard FMJ/TMJ 10mm loads to see if there are feeding problems. They will mostly be a truncated cone or round nosed flat point design. Standard 10mm profiles feed pretty nicely, typically. There are some esoteric options for RN ammo, but hardly the norm.