# Problem #2058

 2058 Which of the cones listed below can be formed from a $252^\circ$ sector of a circle of radius $10$ by aligning the two straight sides? $[asy] import graph; unitsize(1.5cm); defaultpen(fontsize(8pt)); draw(Arc((0,0),1,-72,180),linewidth(.8pt)); draw(dir(288)--(0,0)--(-1,0),linewidth(.8pt)); label("10",(-0.5,0),S); draw(Arc((0,0),0.1,-72,180)); label("252^{\circ}",(0.05,0.05),NE); [/asy]$ $\text{(A) A cone with slant height of } 10 \text{ and radius } 6$ $\text{(B) A cone with height of } 10 \text{ and radius } 6$ $\text{(C) A cone with slant height of } 10 \text{ and radius } 7$ $\text{(D) A cone with height of } 10 \text{ and radius } 7$ $\text{(E) A cone with slant height of } 10 \text{ and radius } 8$ This problem is copyrighted by the American Mathematics Competitions.
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• Reduce fractions to lowest terms and enter in the form 7/9.
• Numbers involving pi should be written as 7pi or 7pi/3 as appropriate.
• Square roots should be written as sqrt(3), 5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
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