2014 AMC 8 Problem 20
Attempt Problem 20 of the 2014 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2014 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
20.
Rectangle has sides and A circle of radius is centered at a circle of radius is centered at and a circle of radius is centered at Which of the following is closest to the area of the region inside the rectangle but outside all three circles?
Answer: B
Small hint:
Inside the rectangle, each circle contributes a quarter-circle sector.
Big hint:
Subtract the total sector area from the rectangle area and approximate .
Solution:
The parts of the three circles inside the rectangle are quarter-circles with radii , , and . Their total area is
Using , this total is about . The rectangle has area , so the desired area is about .
Thus, B is the correct answer.
Problem 20 in other years
- 1985 AMC 8
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