2001 AMC 10 Problem 17

Attempt Problem 17 of the 2001 AMC 10 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2001 AMC 10 solutions, or check the answer key.

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17.

Which of the cones below can be formed from a 252252^\circ sector of a circle of radius 1010 by aligning the two straight sides?

Answer: C
Concepts:conesectorcircumference
Difficulty rating: 1490
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 2523602π10=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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