Compute # of Coins for Tray Inner Rim: Examples

  • Context: High School 
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SUMMARY

This discussion focuses on calculating the number of coins that can fit along the inner rim of a tray based on their respective radii. For a tray with a radius of 6 and coins with a radius of 2, 6 coins fit perfectly. In contrast, a tray with a radius of 8 can accommodate only 1 coin of radius 5. If the coin's radius exceeds the tray's radius, as in the case of a tray with a radius of 4 and a coin of radius 6, no coins can fit. The calculations are based on the principles of circle packing.

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  • Understanding of basic geometry, specifically circle properties.
  • Familiarity with the concept of circle packing.
  • Ability to perform simple arithmetic calculations involving radii.
  • Knowledge of how to interpret visual representations of geometric problems.
NEXT STEPS
  • Research the mathematical principles of circle packing in detail.
  • Explore geometric algorithms for optimizing space usage in circular arrangements.
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Mathematicians, educators, students studying geometry, and anyone interested in optimizing space in circular arrangements.

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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