1997 AMC 8 第 22 题

先试着解答 1997 AMC 8 第 22 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1997 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

22.

一个两英寸的银立方体 (2×2×2)(2\times 2\times 2) 重 33 磅,价值 $200\$ 200。一个三英寸的银立方体价值多少?
A two-inch cube (2×2×2)(2\times 2\times 2) of silver weighs 33 pounds and is worth $200.\$ 200. How much is a three-inch cube of silver worth?
$300\$300
$375\$375
$450\$450
$560\$560
$675\$675
答案:E
知识点:体积长度、面积与体积的缩放关系
小提示:
比较两个立方体中单位立方体的个数
Compare the numbers of unit cubes in the two cubes
大提示:
对同一种材料,价值与体积成正比
Value scales with volume for the same material
解答:
两英寸立方体由 23=82^3 = 8 个单位立方体组成。每个单位立方体价值 200÷8=25 200 \div 8 = 25 美元。三英寸立方体需要 33=273^3 = 27 个单位立方体,所以价值 25⋅27=675 25 \cdot 27 = 675 美元。
所以正确答案是 E。
The two-inch cube consists of 23=82^3 = 8 unit cubes. Each of these unit cubes is worth 200÷8=25 200 \div 8 = 25 dollars. To form a three-inch cube, you need 33=273^3 = 27 unit cubes. This means that it is worth 25⋅27=675 25 \cdot 27 = 675 dollars.
Thus, E is the correct answer.
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