AMC 8 1997 Problem 22

AMC8 1997 年第 22 题

比与比例★★★☆☆

A two-inch cube

(2\times 2\times 2)

of silver weighs 3 pounds and is worth 200 dollars. How much is a three-inch cube of silver worth?

一个 2 英寸的正方体

(2\times 2\times 2)

银块重 3 磅，价值 200 美元。一个三英寸的正方体银块价值多少？

A.300 dollars / 300 美元
B.375 dollars / 375 美元
C.450 dollars / 450 美元
D.560 dollars / 560 美元
E.675 dollars / 675 美元

正确答案 · Correct Answer

解析 · Solution

Solution 1

The two-inch cube has a volume of 8 cubic inches, and the three-inch cube has a volume of 27 cubic inches. Thus, the three-inch cube has a weight that is

\displaystyle \frac{27}{8}

times that of the two-inch cube. Then its value is

\displaystyle \frac{27}{8} \cdot 200 = \text{675 dollars}

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