Question

一家公司用圆柱形罐子销售花生酱。市场研究表明，使用更宽的罐子会增加销量。如果罐子的直径增加 $25\%$ ，而体积不变，那么高度必须减少百分之多少？

A company sells peanut butter in cylindrical jars. Marketing research suggests that using wider jars will increase sales. If the diameter of the jars is increased by $25\%$ without altering the volume, by what percent must the height be decreased?

$10$

$25$

$36$

$50$

$60$

答案：C

知识点：圆柱体积百分数

难度评级：1310

解答：

保持 $\pi r^2 h$ 不变，而半径乘以 $1.25$ ，则高度必须乘以 $\dfrac{1}{1.25^2} = \dfrac{1}{1.5625} = 0.64.$

因此高度变为原来的 $64\%$ ，减少了 $36\%$ 。

所以正确答案是 C。

Keeping $\pi r^2 h$ constant while multiplying the radius by $1.25$ requires the height to be multiplied by $\dfrac{1}{1.25^2} = \dfrac{1}{1.5625} = 0.64.$

So the height becomes $64\%$ of the original, a decrease of $36\%.$

Thus, the correct answer is C.

2004 AMC 10A 第 11 题

答案：C

难度评级：1310

解答：

其他年份的第 11 题