Question

一块均匀密度的薄木片呈边长 $3$ 英寸的等边三角形，重 $12$ 盎司。第二块同种木材、同样厚度、也是等边三角形的木片边长为 $5$ 英寸。下列哪一项最接近第二块木片的重量（盎司）？

A thin piece of wood of uniform density in the shape of an equilateral triangle with side length $3$ inches weighs $12$ ounces. A second piece of the same type of wood, with the same thickness, also in the shape of an equilateral triangle, has side length $5$ inches. Which of the following is closest to the weight, in ounces, of the second piece?

$14.0$

$16.0$

$20.0$

$33.3$

$55.6$

答案：D

知识点：长度、面积与体积的缩放关系比与比例

难度评级：1350

解答：

重量与面积成正比，面积随边长平方缩放。第二块边长是第一块的 $\tfrac53$ 倍，所以重量为 $12\cdot\left(\dfrac53\right)^2=\dfrac{100}{3}\approx33.3$ 盎司。

所以正确答案是 D。

Weight is proportional to area, and area scales with the square of the side length. The second side is $\tfrac53$ times the first, so its weight is $12\cdot\left(\dfrac53\right)^2=\dfrac{100}{3}\approx33.3$ ounces.

Thus, the correct answer is D.

2016 AMC 12B 第 8 题

答案：D

难度评级：1350

解答：

其他年份的第 8 题