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 $25\%$ ，但体积不变，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：圆柱长度、面积与体积的缩放关系百分数

难度评级：1310

解答：

直径乘以 $\tfrac54$ 会使底面积乘以 $\left(\tfrac54\right)^2 = \tfrac{25}{16}$ 。

为保持体积不变，高度必须乘以 $\tfrac{16}{25} = 0.64$ 也就是减少 $1 - 0.64 = 0.36$ ，即 $36\%$ 。

所以正确答案是 C。

Multiplying the diameter by $\tfrac54$ multiplies the base area by $\left(\tfrac54\right)^2 = \tfrac{25}{16}.$

To keep the volume fixed, the height must be multiplied by $\tfrac{16}{25} = 0.64.$ That is a decrease of $1 - 0.64 = 0.36,$ or $36\%.$

Thus, the correct answer is C.

2004 AMC 12A 第 9 题

答案：C

难度评级：1310

解答：

其他年份的第 9 题