Question

下面哪个圆锥可以由一个半径为 $10$ 、圆心角为 $252^\circ$ 的扇形，把两条直边对齐后形成？

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?

答案：C

知识点：圆锥弧圆周长

难度评级：1350

小提示：

扇形的半径会成为圆锥的母线长，所以母线长是 $10$

The radius of the sector becomes the slant height of the cone, so the slant height is $10$

大提示：

扇形的弧长会成为底面周长： $\dfrac{252}{360}\cdot 2\pi(10)$

The arc length of the sector becomes the base circumference: $\dfrac{252}{360}\cdot 2\pi(10)$

解答：

当扇形卷成圆锥时，它的半径 $10$ 成为母线长，它的弧成为底面圆。

弧长为 $\dfrac{252}{360}\cdot 2\pi(10) = \dfrac{7}{10}\cdot 20\pi = 14\pi\text{，}$ 所以底面周长是 $14\pi$ ，底面半径是 $7$ 。

因此该圆锥的底面半径为 $7$ ，母线长为 $10$ ，对应选项 C。

因此，正确答案是 C。

When the sector is rolled into a cone, its radius $10$ becomes the slant height, and its arc becomes the base circle.

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

The cone therefore has base radius $7$ and slant height $10,$ which is choice C.

Thus, the correct answer is C.

2001 AMC 12 第 8 题

答案：C

难度评级：1350

小提示：

大提示：

解答：

其他年份的第 8 题