Difference between revisions of "2008 AMC 8 Problems/Problem 25"
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==Solution== | ==Solution== | ||
− | <cmath>\begin{ | + | <cmath>\begin{array}{c|cc} |
\text{circle #} & radius & area \\ \hline | \text{circle #} & radius & area \\ \hline | ||
1 & 2 & 4\pi \\ | 1 & 2 & 4\pi \\ | ||
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5 & 10 & 100\pi \\ | 5 & 10 & 100\pi \\ | ||
6 & 12 & 144\pi | 6 & 12 & 144\pi | ||
− | \end{ | + | \end{array}</cmath> |
The entire circle's area is <math>144\pi</math>. The area of the black regions is <math>(100-64)\pi + (36-16)\pi + 4\pi = 60\pi</math>. The percentage of the design that is black is <math>\frac{60\pi}{144\pi} = \frac{5}{12} \approx \boxed{\textbf{(A)}\ 42}</math>. | The entire circle's area is <math>144\pi</math>. The area of the black regions is <math>(100-64)\pi + (36-16)\pi + 4\pi = 60\pi</math>. The percentage of the design that is black is <math>\frac{60\pi}{144\pi} = \frac{5}{12} \approx \boxed{\textbf{(A)}\ 42}</math>. |
Revision as of 20:06, 10 March 2015
Problem
Margie's winning art design is shown. The smallest circle has radius 2 inches, with each successive circle's radius increasing by 2 inches. Approximately what percent of the design is black?
Solution
\[\begin{array}{c|cc} \text{circle #} & radius & area \\ \hline 1 & 2 & 4\pi \\ 2 & 4 & 16\pi \\ 3 & 6 & 36\pi \\ 4 & 8 & 64\pi \\ 5 & 10 & 100\pi \\ 6 & 12 & 144\pi \end{array}\] (Error compiling LaTeX. ! You can't use `macro parameter character #' in restricted horizontal mode.)
The entire circle's area is . The area of the black regions is . The percentage of the design that is black is .
See Also
2008 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Last Problem | |
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 AJHSME/AMC 8 Problems and Solutions |
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