Problem
Each member of a research group visited either the Virgin Islands or Hawaii...
|
So What?
Math questions involving two equations and two unknowns can usually be combined into one equation with one unknown.
Petersons.com
|
Add SAT* Tip of the Day to your personalized My Yahoo! page:
About My Yahoo! and RSS »
|
|
|
SAT: Grid-In Question #9 |
|
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
|
, so the total area of the circles |
| (the unshaded area) is four times that, or |
4 |
π |
r2
|
| 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 |
|
|
 |
|
|
π |
|
|
| The number that when divided by |
π |
expresses the ratio of the |
| total area of the square to the total unshaded area is 4. |
|
|
|
