Need Help With Math: Asahi Seiko SA-595 Coin Hopper

[brian23]

I am trying to figure out how much coins can fit into the Asahi Seiko SA-595 Coin Hopper. The US website says that 650 US 5 cent coins can fit in a hopper. How do I figure out how much the coin hopper can hold for $2 Toonie's, $1 Loonies, Canadian 10 cent, US 10 cent, etc?

The reason I am asking is that we use the Asahi Seiko in our Payment Machines for Parking garages and customers are always asking on capacity... I know there has to be a mathematical way.... I tried using this formula to derive the factor

pi * r ^ (2 * h)

So I used this for nickels and I get 31,379.1732

I then took this number and tried creating a formula

31,379.1732 = volume of hopper * 650

This gives me about 48 for volume of hopper. I then tried using this to find the total amount of Canadian dimes it can hold using this formula

and I get 669 then divide by 48 which only gives me 13. This is too low since it is obvious the hopper is large enough to hold more than 13.

What am I doing wrong?

Thanks!

[Jdurg]

First, remember that the volume of a cyliner is pi * (r^2) *h, but I think that could just be a typo in your entry.   

Also keep in mind that a coin is NOT a perfect cylinder and the details in the design make the volume just slightly off when you do your calculations.  As the numbers get bigger, the small error grows as well.

Anyway, if you have 650 coins that fit into there, then the volume of the hopper is equal to the 650 coins multiplied by the volume of one coin.  Granted, the actual hopper will hold more due to those errors mentioned above in your assumptions, but that is the basic formula.

Volume Of US 5-Cent Coin * 650 = Volume of Coin Hopper.

Volume of Coin Hopper / Volume of Desired Coin = # Of Desired Coins It Can Hold.

[brian23]

Figured it out! THANKS!

My parens were off... plus had to use cubic cm!

Seems better now

Canadian $2 Coin: 530 coins
Canadian $1 = 575 coins
Canadian 25 cent = 707 coins
Canadian 10 cent = 1,213 coins
Canadian 5 cent = 715 coins
 
US $1         = 503 coins
US Quarter = 500 coins
US Nickel = 650 coins
US Dime = 1,104 coins

Like you said it can be affected by other factors so the figures are inexact.