To determine how many tiny circles of 2m diameter can fit between the circumferences of the larger and smaller concentric circles, we can proceed as follows:

Step-by-step solution:

1. Radius of each circle:

   • The radius of the smaller circle $r_{\text{small}} = \frac{16}{2} = 8 \, \text{m}$
   • The radius of the larger circle $r_{\text{large}} = \frac{20}{2} = 10 \, \text{m}$
   • The radius of each tiny circle $r_{\text{tiny}} = \frac{2}{2} = 1 \, \text{m}$

2. Width of the annular region (the region between the two circles):

   • The distance between the two circumferences is $r_{\text{large}} - r_{\text{small}} = 10 - 8 = 2 \, \text{m}$

3. Fitting the tiny circles:

   • Since the width of the annular region is exactly $2 \, \text{m}$, the diameter of the tiny circles (2m) matches the width perfectly. This means we can arrange the tiny circles along the circumference of the smaller circle, with their centers aligned along a circle of radius $r_{\text{small}} + 1 = 8 + 1 = 9 \, \text{m}$ (the radius is increased by 1m, which is the radius of the tiny circles).

4. Circumference for the arrangement:

   • The circumference where the centers of the tiny circles will be placed is the circumference of the circle with radius 9m: $C = 2\pi \times 9 = 18\pi \, \text{m}$ This is the path along which we will fit the tiny circles.

5. Number of tiny circles:

   • The circumference occupied by each tiny circle is the length of one of its circumferences (which is the same as its diameter, 2m): $\text{Number of tiny circles} = \frac{C}{2} = \frac{18\pi}{2} = 9\pi \approx 28.27$
   • Since the number of circles must be a whole number, you can fit 28 tiny circles around the circumference between the larger and smaller circles.

Conclusion:

You can fit 28 tiny circles of diameter 2m between the circumferences of the two larger concentric circles.

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Would you like more details on any part of the solution?

Here are 5 related questions to deepen your understanding:

1. How would the result change if the diameter of the larger circle increased?
2. What if the tiny circle diameter was 3 meters instead of 2 meters?
3. Can you fit different-sized circles into the same annular space? If so, how?
4. How would you calculate the remaining space if the circles don’t perfectly fit?
5. What if the two original circles were not concentric?

Tip: For packing problems like this, the key is often in calculating circumferences and considering symmetry in the arrangement.