Problem

2001 AMC 12 Problem 8

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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.


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Category: AMC 12
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