2002 AMC 8 第 13 题

先试着解答 2002 AMC 8 第 13 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 2002 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。

13.

Bert 生日时得到一个盒子,装满时能容纳 125125 颗糖豆。几周后,Carrie 得到一个装满糖豆的更大盒子。她的盒子在高、宽、长三个方向上都是 Bert 盒子的两倍。Carrie 大约得到了多少颗糖豆?
For his birthday, Bert gets a box that holds 125125 jellybeans when filled to capacity. A few weeks later, Carrie gets a larger box full of jellybeans. Her box is twice as high, twice as wide and twice as long as Bert’s. Approximately, how many jellybeans did Carrie get?
250250
500500
625625
750750
10001000
答案:E
知识点:体积长度、面积与体积的缩放关系
小提示:
长、宽、高都加倍,体积乘以 2⋅2⋅22\cdot2\cdot2。
Doubling length, width, and height multiplies volume by 2⋅2⋅2.2\cdot2\cdot2.
大提示:
按体积倍数放大糖豆数量。
Scale the number of jellybeans by the volume factor.
解答:
更大的盒子大约能装 125⋅2⋅2⋅2=1000 125 \cdot 2 \cdot 2 \cdot 2 = 1000 颗糖豆。
所以正确答案是 E。
The larger box will have approximately 125⋅2⋅2⋅2=1000 125 \cdot 2 \cdot 2 \cdot 2 = 1000 jellybeans.
Thus, E is the correct answer.
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