Question

一个等边三角形最初被涂成黑色。每次改变时，每个黑色三角形的中间四分之一变成白色。改变五次后，原来黑色三角形的面积中还剩多少比例是黑色？

An equilateral triangle is originally painted black. Each time the triangle is changed, the middle fourth of each black triangle turns white. After five changes, what fractional part of the original area of the black triangle remains black?

$\dfrac{1}{1024}$

$\dfrac{15}{64}$

$\dfrac{243}{1024}$

$\dfrac14$

$\dfrac{81}{256}$

答案：C

知识点：等比数列面积比

难度评级：1140

解答：

每一次改变都会让当前黑色面积的 $\dfrac34$ 保持黑色。五次改变后，黑色面积比例为 $\left(\dfrac34\right)^5 = \dfrac{243}{1024}.$

所以正确答案是 C。

Each change leaves $\dfrac34$ of the current black area black. After five changes the black fraction is $\left(\dfrac34\right)^5 = \dfrac{243}{1024}.$

Thus, the correct answer is C .

1991 AMC 8 第 25 题

答案：C

难度评级：1140

解答：

其他年份的第 25 题