How much do barbell plates weigh without the hole in the middle?

You probably could get a good estimate by figuring out the area that is missing relative to the total area of the plate.

the thickness is not uniform throughout. would be a bit more complicated to solve than total area.

Engineers secretly add the hole weight to the total weight. As such, it will never be known.

The diameter of the hole with Olympic plates is about 2” or a radius of r=1”, so letting d denote the depth of the hole, it’s volume is pi.r^2d, and letting q denote the density of the filling, the added weight of the filling will be the volume times the density, or pi.r^2dq.

d and q are not standardized, so you’d need that information specifically for the plate in the question.

Not really hard if you know what the plate is made out of.

Measure the missing cylinder height & radius. Volume is pi * radius squared * height. I would assume it's made of iron, which is about .255 lbs per cubic inch, according to google. Add that value to the labeled weight of the plate.

Google says: Barbell sleeves are 50mm, so that's your radius. And 45lb plate is 1.3" thick (33mm). So my rough math says about 4 lbs for the missing hole, which would be 49 lbs for the full plate with out the hole. Math could be off; haven't had any coffee yet.

Don't be such an idiot

Without the hole, they aren't barbell plates.

Very good pre coffee math. Using your numbers for density, thickness of the plate, and diameter of the hole the amount of material removed is about a pound.

Not all have the same size hole. Does your penis easily fit inside it?