Question

Alex 和 Felicia 都养猫。Alex 买的猫粮罐是圆柱形，直径 $6$ 厘米，高 $12$ 厘米。Felicia 买的猫粮罐也是圆柱形，直径 $12$ 厘米，高 $6$ 厘米。Alex 的一个罐头体积与 Felicia 的一个罐头体积之比是多少？

Alex and Felicia each have cats as pets. Alex buys cat food in cylindrical cans that are $6$ cm in diameter and $12$ cm high. Felicia buys cat food in cylindrical cans that are $12$ cm in diameter and $6$ cm high. What is the ratio of the volume of one of Alex's cans to the volume of one of Felicia's cans?

$1:4$

$1:2$

$1:1$

$2:1$

$4:1$

答案：B

知识点：圆柱体积

难度评级：960

视频讲解：

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文字解答：

Felicia 的直径是 Alex 的二倍，所以半径也是二倍，底面积变为四倍。

圆的面积公式是 $\pi r^2$ 。半径加倍时，底面积变为原来的四倍。

因此 Felicia 罐头的底面积是 Alex 罐头的 $4$ 倍。

另一方面，Alex 罐头的高度是 Felicia 罐头的两倍。圆柱体积等于底面积乘高。

所以 Felicia 罐头的体积是 Alex 的 $4 \div 2 = 2$ 倍。

正确答案是 B。

Felicia's diameter is twice as much as Alex's which means that her radius is also twice as much.

Recall that the formula for the area of a circle is $\pi r^2.$ If the radius is doubled, then the area is quadrupled.

This means that the base of Felicia's can has $4$ times the area as the base of Alex's can.

We also see that Alex's can is twice as tall as Felicia's can. The formula for the volume of a can is base times height.

Using this formula, we see that Felicia's can will have twice the volume of Alex's can since $4 \div 2 = 2.$

Thus, the correct answer is B.

2019 AMC 8 第 9 题

答案：B

难度评级：960

视频讲解：

文字解答：

其他年份的第 9 题