2001 AMC 10 Problem 17

Question

Which of the cones below can be formed from a

252^\circ

sector of a circle of radius

10

by aligning the two straight sides?

The sector’s radius becomes the slant height of the cone

The arc length

\dfrac{252}{360}\cdot2\pi\cdot10

becomes the base circumference

2\pi r

When rolled into a cone, the sector’s radius

10

becomes the slant height, and the arc length becomes the base circumference.

The arc length is

\dfrac{252}{360}\cdot2\pi\cdot10=14\pi,

so

2\pi r=14\pi

gives base radius

r=7.

The cone has slant height

10

and base radius

7.

Thus, the correct answer is C.

Problem 17 in other years