Difference between revisions of "2006 AMC 10B Problems/Problem 8"
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== Problem == | == Problem == | ||
− | A | + | A square of area 40 is inscribed in a semicircle as shown. What is the area of the semicircle? |
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− | <math> \ | + | <math> \textbf{(A) } 20\pi\qquad \textbf{(B) } 25\pi\qquad \textbf{(C) } 30\pi\qquad \textbf{(D) } 40\pi\qquad \textbf{(E) } 50\pi </math> |
== Solution == | == Solution == |
Revision as of 12:48, 26 January 2022
Problem
A square of area 40 is inscribed in a semicircle as shown. What is the area of the semicircle?
Solution
Since the area of the square is , the length of a side is . The distance between the center of the semicircle and one of the bottom vertices of the square is half the length of the side, which is .
Using the Pythagorean Theorem to find the radius of the semicircle, . So, the area of the semicircle is .
See Also
2006 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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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