2008 AMC 8 第 21 题

先试着解答 2008 AMC 8 第 21 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 2008 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。

21.

杰里从一个 66 厘米长的圆柱形博洛尼亚香肠中切下一块楔形部分,如虚线曲线所示。哪一个选项最接近这块楔形部分的体积,单位为立方厘米?
Jerry cuts a wedge from a 66-cm cylinder of bologna as shown by the dashed curve. Which answer choice is closest to the volume of his wedge in cubic centimeters?
 48\ 48
 75\ 75
 151\ 151
 192\ 192
 603\ 603
答案:C
知识点:圆柱体积估算
小提示:
圆柱半径为 44 厘米,长度为 66 厘米
The cylinder has radius 44 cm and length 66 cm.
大提示:
虚线切割得到圆柱的一半
The dashed cut takes half the cylinder.
解答:
圆柱直径是 88 厘米,所以半径是 44 厘米。它的长度是 66 厘米。
整个圆柱的体积是 πr2h=π⋅42⋅6=96π\pi r^2h=\pi\cdot4^2\cdot6=96\pi。
虚线切割得到圆柱的一半,所以楔形部分体积为 48π48\pi,约为 151151 立方厘米。
所以正确答案是 C。
The cylinder has diameter 88 cm, so its radius is 44 cm. Its length is 66 cm.
The whole cylinder has volume πr2h=π⋅42⋅6=96π\pi r^2h=\pi\cdot4^2\cdot6=96\pi.
The dashed cut takes half of the cylinder, so the wedge has volume 48π48\pi, which is about 151151 cubic centimeters.
Thus, C is the correct answer.
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