Compute # of Coins for Tray Inner Rim: Examples

  • Thread starter Gianz
  • Start date
In summary, given the radius of the tray and the uniform radius of coins, we can compute the number of coins that can fit in the inner rim of the tray by dividing the tray radius by the coin radius and rounding down to the nearest whole number. If the coin radius is larger than the tray radius, then no coins can fit in the inner rim. This method of packing circles is known as circle packing.
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Gianz
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Given the radius of the tray and the uniform radius of coins, how can we compute for the number of coins that can fit in the inner rim (not the whole tray) of the tray? (see attachment...) :biggrin:
Ex1.
Radius of tray -> 6
Radius of coin -> 2
Ans. 6 coins of size 2 will fit the inner rim of a tray of size 6.
Ex2.
Radius of tray -> 8
Radius of coin -> 5
Ans. 1 coin of size 5 will fit the inner rim of a tray of size 8.
Ex3.
Radius of tray -> 4
Radius of coin -> 6
Ans. Coin cannot fit in tray.
 

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1. What is the purpose of computing the number of coins for tray inner rim?

The purpose of computing the number of coins for tray inner rim is to determine the maximum number of coins that can fit inside the inner rim of a tray. This information is useful for designing trays and containers for storing coins, as it ensures that the inner rim is not too small or too large for the intended number of coins.

2. How do you calculate the number of coins for tray inner rim?

To calculate the number of coins for tray inner rim, you will need to know the diameter of the coins and the inner diameter of the tray. Then, use the formula: Number of Coins = (Inner Diameter of Tray / Diameter of Coins)^2. This formula assumes that the coins are arranged in a perfect circle inside the tray.

3. Can the number of coins for tray inner rim vary for different types of coins?

Yes, the number of coins for tray inner rim can vary for different types of coins. This is because coins can have different diameters, and therefore, the number of coins that can fit inside the inner rim will also differ. It is important to use the correct diameter for the type of coins you are calculating for.

4. What are some examples of calculating the number of coins for tray inner rim?

Here are some examples of calculating the number of coins for tray inner rim:
- If the inner diameter of a tray is 20 cm and the diameter of the coins is 2.5 cm, the number of coins that can fit inside the inner rim is (20/2.5)^2 = 64.
- If the inner diameter of a tray is 15 cm and the diameter of the coins is 3 cm, the number of coins that can fit inside the inner rim is (15/3)^2 = 25.
- If the inner diameter of a tray is 25 cm and the diameter of the coins is 1.5 cm, the number of coins that can fit inside the inner rim is (25/1.5)^2 = 277.78 (rounded down to the nearest whole number).

5. How can I use the calculated number of coins for tray inner rim in practical applications?

The calculated number of coins for tray inner rim can be used in various practical applications, such as designing coin trays for banks or coin collectors, organizing loose change in a piggy bank or cash register, or estimating the number of coins needed for a vending machine or arcade game. It can also be used for educational purposes, such as teaching math concepts or practicing measurement skills.

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