Difference between revisions of "2025 AMC 8 Problems/Problem 12"
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| − | The | + | The region shown below consists of 24 squares, each with side length 1 centimeter. What is the area, in square centimeters, of the largest circle that can fit inside the region, possibly touching the boundaries? |
| + | |||
| + | <asy> | ||
| + | import graph; | ||
| + | |||
| + | size(100); | ||
| + | |||
| + | pen gridPen = black; | ||
| + | |||
| + | void drawSquare(pair p) { | ||
| + | draw(box(p, p + (1,1)), gridPen); | ||
| + | } | ||
| + | |||
| + | int[][] grid = { | ||
| + | {0, 0, 0, 0, 0, 0}, | ||
| + | {0, 0, 1, 1, 0, 0}, | ||
| + | {0, 1, 1, 1, 1, 0}, | ||
| + | {1, 1, 1, 1, 1, 1}, | ||
| + | {1, 1, 1, 1, 1, 1}, | ||
| + | {0, 1, 1, 1, 1, 0}, | ||
| + | {0, 0, 1, 1, 0, 0}, | ||
| + | {0, 0, 0, 0, 0, 0} | ||
| + | }; | ||
| + | |||
| + | int rows = grid.length; | ||
| + | int cols = grid[0].length; | ||
| + | |||
| + | for (int i = 0; i < rows; ++i) { | ||
| + | for (int j = 0; j < cols; ++j) { | ||
| + | if (grid[i][j] == 1) { | ||
| + | drawSquare((j, rows - i - 1)); | ||
| + | } | ||
| + | } | ||
| + | } | ||
| + | </asy> | ||
| + | |||
| + | <math>\textbf{(A)}\ 3\pi\qquad \textbf{(B)}\ 4\pi\qquad \textbf{(C)}\ 5\pi\qquad \textbf{(D)}\ 6\pi\qquad \textbf{(E)}\ 8\pi</math> | ||
Revision as of 20:56, 29 January 2025
The region shown below consists of 24 squares, each with side length 1 centimeter. What is the area, in square centimeters, of the largest circle that can fit inside the region, possibly touching the boundaries?
![[asy] import graph; size(100); pen gridPen = black; void drawSquare(pair p) { draw(box(p, p + (1,1)), gridPen); } int[][] grid = { {0, 0, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0}, {0, 1, 1, 1, 1, 0}, {1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1}, {0, 1, 1, 1, 1, 0}, {0, 0, 1, 1, 0, 0}, {0, 0, 0, 0, 0, 0} }; int rows = grid.length; int cols = grid[0].length; for (int i = 0; i < rows; ++i) { for (int j = 0; j < cols; ++j) { if (grid[i][j] == 1) { drawSquare((j, rows - i - 1)); } } } [/asy]](http://latex.artofproblemsolving.com/2/2/b/22b12d5f528f4fc1b25a685e25d32476c453ec95.png)
