2001 AMC 12 Problem 8

Below is the professionally curated solution for Problem 8 of the 2001 AMC 12, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2001 AMC 12 solutions, or check the answer key.

All of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:conearccircumference

Difficulty rating: 1350

8.

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?

Solution:

When the sector is rolled into a cone, its radius 1010 becomes the slant height, and its arc becomes the base circle.

The arc length is 2523602π(10)=71020π=14π, \dfrac{252}{360}\cdot 2\pi(10) = \dfrac{7}{10}\cdot 20\pi = 14\pi, so the base circumference is 14π14\pi and the base radius is 7.7.

The cone therefore has base radius 77 and slant height 10,10, which is choice C.

Thus, the correct answer is C.

Problem 8 in Other Years