Sunday: dimes or quarters?

The pregnancy center in our area has an interesting fundraiser. Every year they give a bunch of baby bottles to churches and then members take them home and fill them will change (or dollars). It's a nice way to get rid of the spare change that we've accumulated during the year and help out the organization.

While I was putting coins in, I noticed that the dimes felt so much smaller than the quarters. It made me wonder: would it be better to put only dimes in the baby bottles or only quarters? My guess is quarters. But what if weight is a factor? Then would it be better to do dimes or quarters?

So off to do some math. But I started out at the US Mint, where they give handy facts about the coins. (If you don't care about the math, you can go to the end for the tl;dr) (Too long; didn't read)

A dime has a volume of 340.0964 mm^3.

So lets see what a quarter's volume would be if it were equal to that of a dime:

340.0964 mm^3/dime * 2.5 dimes/quarters = 850.241 mm^3

A quarter has an actual volume of 808.9035 mm^3, so if space were perfectly utilized, quarters would be better to put in the baby bottle.

But you can't fill up the baby bottle perfectly, so this becomes a packing problem. I think the baby bottle was about 2" in diameter. We'll estimate that you can get three quarters per row (you can't quite get three flat quarters, but if you put some in vertically it is probably close). We will estimate that you can get seven dimes per layer. If the baby bottle was 35mm (7" tall), we would get 331 dimes or 184 quarters in the bottle. Oh, quarters won again with $46 to $33 for dimes.

However, the bottle of quarters would be about 25% heavier than the one of dimes.

tl;dr

If people want you to fill up a baby bottle with coins, putting only quarters in the bottle would be better than putting in only dimes. My hypothesis was correct.