if you had a five gallon bucket of quarters and a five gallon bucket of dimes?

Question

wich bucket wouldcontain the most money

ok idon't mean mass or voulum i mean dallor wise how much money

Answer 1

Good question. First there is the question of how much volume there is in a dime vs. a quarter. You would need 2.5 dimes in the same space as a quarter.

Let's say a quarter is about 50% thicker than a dime (1.5) and the diameter is about 33% bigger than a dime (1.333).

Then the volume would be 1.5 x 1.333 x 1.333 times as much.

3/2 x 4/3 x 4/3 = 8/3 = 2 2/3.

So the quarter is equivalent to about 2 and 2/3 dimes in terms of volume. However, I'd need to find exact measurements and also have to account for spaces between coins, etc.

My gut feeling is the bucket of dimes would contain the most money.

Okay, I checked some figures on Wikipedia:

Quarter:
24.26 mm thickness
1.75 mm diameter

Dime:
17.91 mm thickness
1.35 mm diameter

Ratio of thickness 24.26 / 17.91 = 1.35455...
Ratio of diameter 1.75 / 1.35 = 1.296296...

Ratio of volume = 1.35455 x 1.296296 x 1.296296
= 2.276

So a quarter is equivalent in volume to 2.276 dimes (22.76 cents), so I was wrong.

This would imply that the five gallon bucket of quarters would contain the most money
.
I'm now puzzled about the space between coins, and how that matters. Certainly dimes can pack closer together compared to quarters so does that offset the volume difference? Ack, you've got a puzzling question there and I'm very curious on the final answer.

Edit:

Okay, I've returned. Looking further at the numbers on Wikipedia, it appears that the actual composition of the quarter and dime are equivalent. And as has been noted, the masses of each correspond to their value. A quarter weighs exactly 2.5 times as much as a dime. (Similarly a half-dollar weighs exactly 2 times as much as a quarter.)

Given equal densities and masses equal to their value, that would say that they should be equal. However, now we are back to the vagaries of packing. Given their smaller size and smaller thickness, I think the dime would now have the edge in the packing arena. So I once again say that you would have slightly more value in the bucket filled with dimes versus the bucket filled with quarters.

Answer 2

It depends on how much room the quarters and nickles take up. Since a quarter is 5* the value of a nickle, the nickle would have to take up 1/5 of the room that a quarter does for there to be the same amount of money in each bucket. I'd say that a nickle is at least 1/2 the size of a quarter, so the quarter bucket has more money

Answer 3

They're equal.

Back in the days when we had actual silver dollars, half dollars, quarters and dimes, a dollar was an ounce of silver, and each of the other coins was 1/2, 1/4, and 1/10th of an ounce, respectively.

Today, although the metal used is non-precious, a quarter still weighs as much as 2.5 dimes.

Answer 4

I believe that it would be the quarter. While the dime is smaller, I do not believe that it is enough smaller to make up the difference. Be an interesting experiment. Even more interesting would be the formula. Quarter is x diameter and y thickness to dimes r diameter and s thickness.

Answer 5

The bucket with dimes. Since dimes weigh less, you'd have more dimes than nickels. It also helps that the dimes are physically smaller and are worth twice as much.

US Coinage
Penny Standard weight 2.5 grams
Nickel Standard weight 5.0 grams
Dime Standard weight 2.268 grams
Quarter Standard weight 5.670 grams

Answer 6

a dime takes up about one third the volume of a quarter. the dime bucket will have more money

Answer 7

This is a bit more complex than one would suspect to prove. The topic to research this is called "random close packing". The guess would be that the quarters are a denser form of money in the situation you describe.

Answer 8

Obviously no one is reading the question. Where do you see anything about 5 cent pieces anywhere in the question?

Quarters and dimes. PERIOD.

Answer 9

LMAO he never said any of the buckets had NICKLES silly heads!