Difference between revisions of "1996 AHSME Problems/Problem 27"

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==Problem==
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Consider two solid spherical balls, one centered at <math> (0, 0,\frac{21}{2}) </math> with radius <math>6</math>, and the other centered at <math> (0, 0, 1) </math> with radius <math>\frac{9}{2}</math>. How many points with only integer coordinates (lattice points) are there in the intersection of the balls?
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<math> \text{(A)}\ 7\qquad\text{(B)}\ 9\qquad\text{(C)}\ 11\qquad\text{(D)}\ 13\qquad\text{(E)}\ 15 </math>
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==See also==
 
==See also==
 
{{AHSME box|year=1996|num-b=26|num-a=28}}
 
{{AHSME box|year=1996|num-b=26|num-a=28}}

Revision as of 13:20, 19 August 2011

Problem

Consider two solid spherical balls, one centered at $(0, 0,\frac{21}{2})$ with radius $6$, and the other centered at $(0, 0, 1)$ with radius $\frac{9}{2}$. How many points with only integer coordinates (lattice points) are there in the intersection of the balls?

$\text{(A)}\ 7\qquad\text{(B)}\ 9\qquad\text{(C)}\ 11\qquad\text{(D)}\ 13\qquad\text{(E)}\ 15$

See also

1996 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 26
Followed by
Problem 28
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