2001 AMC 8 第 9 题

先试着解答 2001 AMC 8 第 9 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 2001 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。

9.

大风筝要覆盖金箔。金箔从一张刚好覆盖整个方格的长方形纸上裁出。从四个角裁掉的废料有多少平方英寸?
The large kite is covered with gold foil. The foil is cut from a rectangular piece that just covers the entire grid. How many square inches of waste material are cut off from the four corners?
6363
7272
180180
189189
264264
答案:D
知识点:长度、面积与体积的缩放关系面积筝形
小提示:
高和宽都扩大三倍,面积扩大 99 倍
Tripling both dimensions multiplies area by 99
大提示:
废料面积等于大风筝面积
The waste area equals the large kite area
解答:
整个方格的面积是 3⋅7⋅3⋅6=378。 3 \cdot 7 \cdot 3 \cdot 6 = 378\text{。}由风筝面积公式,风筝面积是这个面积的一半,所以废料面积为 378÷2=189378 \div 2 = 189。
所以正确答案是 D。
The area of the entire grid would be 3⋅7⋅3⋅6=378. 3 \cdot 7 \cdot 3 \cdot 6 = 378. The area of the kite is one-half this area from the formula for the area of the kite, so the wasted material is 378÷2=189.378 \div 2 = 189.
Thus, D is the correct answer.
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