Difference between revisions of "2006 AMC 10B Problems/Problem 6"
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Revision as of 11:17, 4 July 2013
Problem
A region is bounded by semicircular arcs constructed on the side of a square whose sides measure , as shown. What is the perimeter of this region?
Solution
Since the side of the square is the diameter of the semicircle, the radius of the semicircle is .
Since the length of one of the semicircular arcs is half the circumference of the corresponding circle, the length of one arc is .
Since the desired perimeter is made up of four of these arcs, the perimeter is .
See Also
2006 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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 AMC 10 Problems and Solutions |
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