Problem
Jennifer has a mixture that is 4 cups cinnamon and 1 cup sugar, and she wants it to be 3 parts cinnamon to 1 part sugar...
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SAT: Grid-In Question #9 |
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Question:
| In the figure above, 4 identical circles are tangent to each other |
| and the sides of the square. |
| What number, when divided by |
π |
, expresses the ratio of the |
| total area of the square to the total unshaded area? |
| No numbers are given, but let |
r |
equal the radius of each circle. The |
| area of a circle is equal to |
π |
r2
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, so the total area of the circles |
| (the unshaded area) is four times that, or |
4 |
π |
r2
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| Now look at the square. Each side of the square is really the |
| length of 4 radii, or |
4 |
r |
, so the total area of the square is equal to |
| So the ratio of the total area of the square to the total unshaded |
|
4 |
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|
π |
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| The number that when divided by |
π |
expresses the ratio of the |
| total area of the square to the total unshaded area is 4. |
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