It’s in the kitchen gadget drawer… White plastic spherical “paddle wheel” with 8 paddles about the size of a golf ball.
Could it be something to help mix liquids in shake containers? I see this on Amazon.
That was my guess, too. They make good cat toys 
Bingo! It’s going to be a cat toy.
The cat is not impressed.
They never are if you just give it to them. If they steal it (especially when you’re trying to use it), then it’s the most excellent kitty toy EVER.
Wow, that is not at all what I envisioned based on the OP. Good guessing.
Thanks! I have over 40 years’ worth of kitchen gadgets stowed away, and I inherited a drawerful from both my mother and mother-in-law. I am a fount of information about any number of kitchen tools of dubious utility!
(Drop the thing on the floor in front of the cat, as if by accident, and then walk away.)
4 gallon capacity.
They don’t look anywhere near that big. 
there’s a forum on reddit dedicated to this issue:
Yeah, also, got a pic? Ideally a pic with a fiducial for scale.
Did it come in a box?
I have no idea where it came from. I most certainly have not purchased any of the aforementioned Shaker balls.
A few days Linden was batting around what looks like a tiny version of a shaker bottle ball, but probably 1/2 the size of the shaker balls I actually own. I also have no idea what it is, but I suspect it’s a toy, not a kitchen item.
Yeah, you have to leave it out on the counter over night. That’s the true test.