In fairness, the Empire State Building is mostly empty space. If what you have is elemental carbon, the same mass is a cube with 6m sides.

Which, yes, you then need 30,000 of so it doesn't make the whole thing that much easier.

10B tons of C is a mere 10 cubic kilometers. For context, we have individual open pit mines of over 2 cubic kilometers.

If we had emitted 37 billion metric tons of CO2 a year each year for the last 400 years that would be a total of about 1.48 x 10^19 grams of CO2. That's more than we now have in the atmosphere so this gives us a convenient upper limit.

12/44th of the mass of CO2 is from carbon, so that is 4 x 10^18 g of carbon to deal with if we wanted to store all the carbon current in atmospheric CO2.

The density of carbon depends on what form it is in--diamond is a lot denser than graphite, which is a lot denser than carbon powder. Let's store it as graphite, which has a density of 2.2 g/cm^3.

We'd need 1.8 x 10^18 cm^3 for that much powdered carbon, or 1.8 x 10^12 m^3, or 1800 km^3.

But remember that we are getting all this carbon we need to deal with using energy from massive solar farms. Put the solar panels a few meters off the ground, and dump the graphite under the solar panels. If the graphite was dumped into a pile 1 m tall it would need 1800 km^2 of area.

That would be just a tiny fraction of the area available under the amount of panels we'd have to be using to capture that much carbon. Spread evenly under all the panels it would be less than a millimeter.