Question

如图，一个区域由以边长为 $\tfrac{2}{\pi}$ 的正方形各边为直径构造的半圆弧围成。这个区域的周长是多少？

A region is bounded by semicircular arcs constructed on the sides of a square whose sides measure $\tfrac{2}{\pi},$ as shown. What is the perimeter of this region?

$\dfrac{4}{\pi}$

$2$

$\dfrac{8}{\pi}$

$4$

$\dfrac{16}{\pi}$

答案：D

知识点：弧周长圆周长

难度评级：1060

解答：

每条边长为 $\tfrac{2}{\pi}$ ，也是一个半圆弧的直径，所以每条弧长为 $\tfrac12\pi\cdot\tfrac{2}{\pi}=1$ 。

边界由四条这样的弧组成，所以周长为 $4\cdot1=4$ 。

所以正确答案是 D。

Each side has length $\tfrac{2}{\pi},$ the diameter of a semicircular arc, so each arc has length $\tfrac12\pi\cdot\tfrac{2}{\pi}=1.$

The boundary consists of four such arcs, so the perimeter is $4\cdot1=4.$

Thus, the correct answer is D.

2006 AMC 10B 第 6 题

答案：D

难度评级：1060

解答：

其他年份的第 6 题