2001 AMC 10 Problem 17

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.