Difference between revisions of "2016 AMC 12B Problems/Problem 18"
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<math>(x - \frac{1}{2})^2+(y - \frac{1}{2})^2=\frac{1}{2}</math>. | <math>(x - \frac{1}{2})^2+(y - \frac{1}{2})^2=\frac{1}{2}</math>. | ||
Notice the circle intersect the axe at point <math>(0, 1)</math> and <math>(1, 0)</math>. Find the area of this circle in the first quadrant. The area is made of a semi-circle and a triangle: | Notice the circle intersect the axe at point <math>(0, 1)</math> and <math>(1, 0)</math>. Find the area of this circle in the first quadrant. The area is made of a semi-circle and a triangle: | ||
− | <math>\frac{ | + | <math>\frac{\pi}{4} +\frac{1}{2}</math> |
Because of symmetry, the area is the same in all four quadrants. | Because of symmetry, the area is the same in all four quadrants. | ||
The answer is <math>\boxed{\textbf{(B)}\ 2 + \pi}</math> | The answer is <math>\boxed{\textbf{(B)}\ 2 + \pi}</math> |
Revision as of 21:22, 21 February 2016
Problem
What is the area of the region enclosed by the graph of the equation
Solution
Consider the case when . . . Notice the circle intersect the axe at point and . Find the area of this circle in the first quadrant. The area is made of a semi-circle and a triangle: Because of symmetry, the area is the same in all four quadrants. The answer is
See Also
2016 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 17 |
Followed by Problem 19 |
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 12 Problems and Solutions |
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