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  3. [img]ct_gre5image038[/img]A rectangular label is attached to a right circular c

[img]ct_gre5image038[/img]A rectangular label is attached to a right circular c

游客2025-02-24  1
问题
A rectangular label is attached to a right circular cylinder with radius r. The label, which encircles the cylinder without overlap, has width w and an area equal to the area of the base of the cylinder.

Column A                   Column B
w                          r
选项 A、if the quantity in Column A is greater
B、if the quantity in Column B is greater
C、if the two quantity are equal
D、if the relationship cannot be determined from the information given
答案 B
解析 一个长方形的检签贴在半径为r的直圆柱上。该标签围绕圆柱体一周且不重叠，其宽度为训，面积等于圆柱体底面的面积。
解：本题的正确答案为(B)。由于该标签围绕圆柱体且不重叠，所以其长度等于圆柱体底面的周长=2∏r，则其面积=2∏r×w(因为这是一个长方形标签)，圆柱体底面积为∏r2，由题意可得：2∏r×w=∏r2→ w=r/2
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