How many marbles fit in the capitol building?

Answer 1

No one has accurately estimated the interior volume of the entire US Capitol, however, we do know the volume of the central rotunda.

The Rotunda is a circular room in the center of the building beneath the Capitol dome. It is 96 feet in diameter and rises 180 feet from the floor to the canopy, with a volume of approximately 1.3 million cubic feet.

So how many marbles can fit in the Rotunda? A Lot.

Seriously, here is the math.

First som assumptions need to be defined.

Marbles are assumed to be regular spheres of constant size.

Marbles will pack into a closest pack arrangement. This assumes 26% of the volume is wasted (i.e. the gaps between the closely packed spheres).

Assume each marble is 1/2 inch in diameter.

Volume of a sphere is 4/3 *pi * radius cubed

V = 1.33333 * 3.14159 * .25 *.25 * .25
V = 0.065449628 inches cubed.

Converting this to cubic feet we get
V = 3.78759421 × 10-5 cubic feet

Now calculate the "wasted space" in the Rotundra as 24% we get
Avail Vol = 76% * 1.3 million cubic feet
Avail Vol = 988,000 cubic feet.

Dividing Avail Vol by the vol of each marble and we get...

n = 988000 / 3.78759421 × 10-5
n= 2.60851597 × 1010 marbles

As I said before, that's a lot of marbles