2019 AMC 8 第 9 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
9.
Alex 和 Felicia 都养猫。Alex 买的猫粮罐是圆柱形，直径 厘米，高 厘米。Felicia 买的猫粮罐也是圆柱形，直径 厘米，高 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 cm in diameter and cm high. Felicia buys cat food in cylindrical cans that are cm in diameter and cm high. What is the ratio of the volume of one of Alex’s cans to the volume of one of Felicia’s cans?
小提示：
圆柱体积为
Volume is
大提示：
Felicia 的半径加倍，高度减半
Felicia’s radius doubles while her height halves
视频讲解：
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文字解答：
Felicia 罐头的直径是 Alex 罐头的两倍，这说明她的罐头半径也是两倍。
圆的面积公式是 。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 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 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 If the radius is doubled, then the area is quadrupled.
This means that the base of Felicia’s can has 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
Thus, the correct answer is B.
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