Difference between revisions of "1972 AHSME Problems/Problem 28"
Coolmath34 (talk | contribs) (Created page with "== Problem 28 == A circular disc with diameter <math>D</math> is placed on an <math>8\times 8</math> checkerboard with width <math>D</math> so that the centers coincide. The...") |
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==Solution== | ==Solution== | ||
| − | Consider the upper right half of the grid, which consists of a | + | Consider the upper right half of the grid, which consists of a <math>4\times4</math> section of the checkerboard and a quarter-circle of radius <math>4</math>. We can draw this as a coordinate grid and shade in the complete squares. There are <math>8</math> squares in the upper right corner, so there are <math>8 \cdot 4 = \boxed{32}</math> whole squares in total. |
The answer is <math>\textbf{(E)}.</math> | The answer is <math>\textbf{(E)}.</math> | ||
-edited by coolmath34 | -edited by coolmath34 | ||
Latest revision as of 12:53, 23 June 2021
Problem 28
A circular disc with diameter 
is placed on an 
checkerboard with width so that the centers coincide. The number of checkerboard squares which are completely covered by the disc is
Solution
Consider the upper right half of the grid, which consists of a 
section of the checkerboard and a quarter-circle of radius 
. We can draw this as a coordinate grid and shade in the complete squares. There are 
squares in the upper right corner, so there are 
whole squares in total.
The answer is 
-edited by coolmath34
