Packing Intuition Math Example 1

Solution

1. 1
   Step 1: Each coin occupies a $2\,\text{cm}\times 2\,\text{cm}$ square cell. Number per row $= 10/2 = 5$. Total coins $= 5 \times 5 = 25$.
2. 2
   Step 2: Area of each coin $= \pi(1)^2 = \pi$ cm$^2$. Total coin area $= 25\pi$ cm$^2$.
3. 3
   Step 3: Tray area $= 100$ cm$^2$. Packing efficiency $= \dfrac{25\pi}{100} = \dfrac{\pi}{4} \approx 78.5\%$.