options: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).

Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
problem_activity: Task
Below is a table of diameters of different denominations of United States
Coins:
| Denomination | Diameter  |
|--------------|-----------|
|     Dime     | $17.9$ mm |
|    Nickel    | $21.2$ mm |
|   Quarter    | $24.3$ mm |
| Half Dollar  | $30.6$ mm |
If we place nickels around a central dime, as in the picture below, there is room
for five nickels with extra space but not enough room for a sixth nickel:
[IMG]
How many dimes fit around a central dime?  What about around a
central nickel, quarter, or half dollar?  Do the dimes fit snugly or is there
extra space?
How many half dollars fit around a central dime?  What about around
a central nickel, quarter, or half dollar?  Do the half dollars fit snugly or
is there extra room?
Extending the work in (a) and (b) above, for positive numbers $r$ and $s$
how many circles of radius $s$ will fit around a central circle of radius $r$?


correct_option_index: 0

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