AMC10 2001 A

AMC10 2001 A · Q17

AMC10 2001 A · Q17. It mainly tests 3D geometry (volume).

Which of the cones below can be formed from a 252° sector of a circle of radius 10 by aligning the two straight sides?

下面哪个圆锥可以由半径为10的圆的252°扇形通过将两条直边对齐而成？

(A)

(B)

(C)

(D)

(E)

Answer

Correct choice: (C)

正确答案：（C）

Solution

(C) The slant height of the cone is 10, the radius of the sector. The circumference of the base of the cone is the same as the length of the sector’s arc. This is $252/360 = 7/10$ of the circumference, $20\pi$, of the circle from which the sector is cut. The base circumference of the cone is $14\pi$, so its radius is 7.

（C）圆锥的斜高为 10，即扇形的半径。圆锥底面的周长等于扇形弧长。这段弧长是从中切出扇形的圆的周长 $20\pi$ 的 $252/360 = 7/10$。因此圆锥底面周长为 $14\pi$，其底面半径为 7。

Topics

GE.013 3D geometry (volume)