AMC8 2019

AMC8 2019 · Q9

AMC8 2019 · Q9. It mainly tests Ratios & proportions, 3D geometry (volume).

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?

Alex 和 Felicia 都养猫作为宠物。Alex 买的猫粮罐是直径 $6$ cm、高 $12$ cm 的圆柱体。Felicia 买的猫粮罐是直径 $12$ cm、高 $6$ cm 的圆柱体。Alex 的一个罐的体积与 Felicia 的一个罐的体积的比是多少？

(A) 1:4 1:4

(B) 1:2 1:2

(D) 2:1 2:1

(E) 4:1 4:1

Answer

Correct choice: (B)

正确答案：（B）

Solution

Using the formula for the volume of a cylinder $\pi r^2 h$, we get Alex, $108\pi$, and Felicia, $216\pi$. We can quickly notice that $\pi$ cancels out on both sides and that Alex's volume is $1/2$ of Felicia's leaving $1/2 = \boxed{\textbf{(B)}\ 1:2}$ as the answer.

使用圆柱体积公式 $\pi r^2 h$，Alex 为 $108\pi$，Felicia 为 $216\pi$。$\pi$ 两边抵消，Alex 的体积是 Felicia 的一半，因此比为 $\boxed{\textbf{(B)}\ 1:2}$。

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