Difference between revisions of "1992 AJHSME Problems/Problem 5"
5849206328x (talk | contribs) (Created page with '==Problem== A circle of diameter <math>1</math> is removed from a <math>2\times 3</math> rectangle, as shown. Which whole number is closest to the area of the shaded region? <…') |
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Latest revision as of 23:09, 4 July 2013
Problem
A circle of diameter 
is removed from a 
rectangle, as shown. Which whole number is closest to the area of the shaded region?
![[asy] fill((0,0)--(0,2)--(3,2)--(3,0)--cycle,gray); draw((0,0)--(0,2)--(3,2)--(3,0)--cycle,linewidth(1)); fill(circle((1,5/4),1/2),white); draw(circle((1,5/4),1/2),linewidth(1)); [/asy]](http://latex.artofproblemsolving.com/1/c/8/1c8b52d197731b410838a3439b6b219ae443fe19.png)
Solution
The area of the shaded region is the area of the circle subtracted from the area of the rectangle.
The diameter of the circle is , so the radius is 
and the area is
![\[(1/2)^2\pi = \pi /4.\]](http://latex.artofproblemsolving.com/e/7/c/e7c589a17e10c0952745477eb43c5549d1fa58e7.png)
The rectangle obviously has area 
, so the area of the shaded region is 
.
This is closest to 
.
See Also
| 1992 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
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