<h2>Problem 28</h2> <p>A circular disc with diameter <img alt="$D$" height="14" src="https://latex.artofproblemsolving.com/9/f/f/9ffb448918db29f2a72f8f87f421b3b3cad18f95.png" width="17" /> is placed on an <img alt="$8\times 8$" height="12" src="https://latex.artofproblemsolving.com/1/9/7/1970593e80703dfe31ef799575bae2ee9819ced1.png" width="40" /> checkerboard with width <img alt="$D$" height="14" src="https://latex.artofproblemsolving.com/9/f/f/9ffb448918db29f2a72f8f87f421b3b3cad18f95.png" width="17" /> so that the centers coincide. The number of checkerboard squares which are completely covered by the disc is</p> <p><img alt="$\textbf{(A) }48\qquad \textbf{(B) }44\qquad \textbf{(C) }40\qquad \textbf{(D) }36\qquad \textbf{(E) }32$" height="17" src="https://latex.artofproblemsolving.com/6/2/9/629826d873a2586193d48091b38b8b9efadd9b08.png" width="398" /></p>

Question No: 472

Problem 28

A circular disc with diameter $D$ is placed on an $8\times 8$ checkerboard with width $D$ so that the centers coincide. The number of checkerboard squares which are completely covered by the disc is

$\textbf{(A) }48\qquad \textbf{(B) }44\qquad \textbf{(C) }40\qquad \textbf{(D) }36\qquad \textbf{(E) }32$

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Tags: Geometry

Question Details

Problem 28