2010 AMC 8 Problems/Problem 18
Problem
A decorative window is made up of a rectangle with semicircles at either end. The ratio of to is . And is 30 inches. What is the ratio of the area of the rectangle to the combined area of the semicircles?
Solution
We can set a proportion:
We substitute with 30 and solve for .
We calculate the combined area of semicircle by putting together semicircle and to get a circle with radius . Thus, the area is . The area of the rectangle is . We calculate the ratio:
Note that we could have solved this without the measurement of inches.
Video Solution by OmegaLearn
https://youtu.be/j3QSD5eDpzU?t=657
~ pi_is_3.14
Video by MathTalks
https://www.youtube.com/watch?v=KSYVsSJDX-0&feature=youtu.be
See Also
2010 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.