2014 AMC 8 Problems/Problem 20
Problem
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?
Solution
The area in the rectangle but outside the circles is the area of the rectangle minus the area of all three of the quarter circles in the rectangle.
The area of the rectangle is . The area of all 3 quarter circles is . Therefore the area in the rectangle but outside the circles is . is approximately and substituting that in will give
Video Solution
https://youtu.be/e4gDE2uLQ6A ~DSA_Catachu
https://youtu.be/EPILwH5iA9Q ~savannahsolver
Video Solution by OmegaLearn
https://youtu.be/j3QSD5eDpzU?t=2327
~ pi_is_3.14
See Also
2014 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.