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2001 AMC 10 Problem 17

Problem 17 of 25IntermediateGeometry

Which of the cones below can be formed from a 252∘252^\circ sector of a circle of radius 1010 by aligning the two straight sides?

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Solution

When rolled into a cone, the sector’s radius 1010 becomes the slant height, and the arc length becomes the base circumference. The arc length is 252360⋅2π⋅10=14π,\dfrac{252}{360}\cdot2\pi\cdot10=14\pi, so 2πr=14π2\pi r=14\pi gives base radius r=7.r=7. The cone has slant height 1010 and base radius 7.7. Thus, the correct answer is C.
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Tagged: cone · sector · circumference

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