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AMC12每日一题(2001年真题#04)

2018-05-30
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2001 AMC 12竞赛试题/第04题

Problem

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(

$\text{(A) A cone with slant height of } 10 \text{ and radius } 6$

$\text{(B) A cone with height of } 10 \text{ and radius } 6$

$\text{(C) A cone with slant height of } 10 \text{ and radius } 7$

$\text{(D) A cone with height of } 10 \text{ and radius } 7$

$\text{(E) A cone with slant height of } 10 \text{ and radius } 8$

Solution

[asy] import graph; unitsize(1.5cm); defaultpen(fontsize(8pt)); draw(Arc((0,0),1,-72,180),linewidth(.8pt) + red); draw(dir(288)--(0,0)--(-1,0),linewidth(.8pt) + blue); label(

The blue lines will be joined together to form a single blue line on the surface of the cone, hence $\boxed{10}$ will be the $\boxed{\text{slant height}}$ of the cone.