Question

两个直圆柱的体积相同。第二个圆柱的半径比第一个圆柱的半径大 $10\%$ 。这两个圆柱的高之间有什么关系？

Two right circular cylinders have the same volume. The radius of the second cylinder is $10\%$ more than the radius of the first. What is the relationship between the heights of the two cylinders?

第二个高比第一个少 $10\%$ 。

The second height is $10\%$ less than the first.

第一个高比第二个多 $10\%$ 。

The first height is $10\%$ more than the second.

第二个高比第一个少 $21\%$ 。

The second height is $21\%$ less than the first.

第一个高比第二个多 $21\%$ 。

The first height is $21\%$ more than the second.

第二个高是第一个的 $80\%$ 。

The second height is $80\%$ of the first.

答案：D

知识点：圆柱体积百分数

难度评级：1380

解答：

设第一个和第二个圆柱的半径、高分别为 $r,h$ 和 $R,H$ 。体积相等，所以 $\pi r^2 h = \pi R^2 H$ ，且 $R = 1.1r$ 。

则 $\pi r^2 h = \pi(1.1r)^2 H$ $= \pi(1.21 r^2) H$ 。除以 $\pi r^2$ 得 $h = 1.21H$ ，所以第一个高比第二个多 $21\%$ 。

因此，正确答案是 D。

Let $r,h$ and $R,H$ be the radii and heights of the first and second cylinders. The volumes are equal, so $\pi r^2 h = \pi R^2 H,$ and $R = 1.1r.$

Then $\pi r^2 h = \pi(1.1r)^2 H$ $= \pi(1.21 r^2) H.$ Dividing by $\pi r^2$ yields $h = 1.21H,$ so the first height is $21\%$ more than the second.

Thus, the correct answer is D.

2015 AMC 12A 第 7 题

答案：D

难度评级：1380

解答：

其他年份的第 7 题