To solve this, we will calculate how many 8mm diameter balls (which form circles in 2D) can fit in a 7 cm by 10 cm rectangle.

Step 1: Convert all measurements to the same unit.

• Diameter of each ball: $8 \text{mm} = 0.8 \text{cm}$
• Width of the rectangle: $7 \text{cm}$
• Length of the rectangle: $10 \text{cm}$

Step 2: Calculate how many balls fit along each dimension.

• Number of balls along the width: $\text{Number of balls along width} = \frac{7 \text{ cm}}{0.8 \text{ cm/ball}} = 8.75$ This rounds down to 8 balls.

• Number of balls along the length: $\text{Number of balls along length} = \frac{10 \text{ cm}}{0.8 \text{ cm/ball}} = 12.5$ This rounds down to 12 balls.

Step 3: Calculate the total number of balls.

Now multiply the number of balls that fit along each dimension: $\text{Total number of balls} = 8 \times 12 = 96$

Thus, 96 balls can fit in the rectangle.

Would you like more details on the arrangement or any other questions? Here are 5 related questions:

1. How would the result change if the balls were arranged in a hexagonal pattern?
2. How does changing the ball diameter affect the number that fit?
3. What happens if we include the space between the balls in the calculation?
4. Can we fit a different number of balls if we allow partial balls at the edges?
5. How would the packing efficiency change in a 3D scenario?

Tip: Always account for the possibility of different packing arrangements (e.g., rectangular or hexagonal) when calculating the maximum number of objects in a given space.