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Difference between revisions of "2025 AMC 8 Problems/Problem 12"

m (Protected "2025 AMC 8 Problems/Problem 12" ([Edit=Allow only administrators] (expires 17:59, 29 January 2025 (UTC)) [Move=Allow only administrators] (expires 17:59, 29 January 2025 (UTC))))
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The 2025 AMC 8 is not held yet. Please do not post false problems.
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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?
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<asy>
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import graph;
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size(100);
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pen gridPen = black;
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void drawSquare(pair p) {
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    draw(box(p, p + (1,1)), gridPen);
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}
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int[][] grid = {
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    {0, 0, 0, 0, 0, 0},
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    {0, 0, 1, 1, 0, 0},
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    {0, 1, 1, 1, 1, 0},
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    {1, 1, 1, 1, 1, 1},
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    {1, 1, 1, 1, 1, 1},
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    {0, 1, 1, 1, 1, 0},
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    {0, 0, 1, 1, 0, 0},
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    {0, 0, 0, 0, 0, 0}
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};
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int rows = grid.length;
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int cols = grid[0].length;
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for (int i = 0; i < rows; ++i) {
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    for (int j = 0; j < cols; ++j) {
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        if (grid[i][j] == 1) {
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            drawSquare((j, rows - i - 1));
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        }
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    }
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}
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</asy>
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<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]

$\textbf{(A)}\ 3\pi\qquad \textbf{(B)}\ 4\pi\qquad \textbf{(C)}\ 5\pi\qquad \textbf{(D)}\ 6\pi\qquad \textbf{(E)}\ 8\pi$

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