AMC8 1997

AMC8 1997 · Q22

AMC8 1997 · Q22. It mainly tests Ratios & proportions, 3D geometry (volume).

A two-inch cube (2 × 2 × 2) of silver weighs 3 pounds and is worth $200. How much is a three-inch cube of silver worth?

一个 2 英寸的银立方体（$2 \times 2 \times 2$）重 3 磅，价值 200 美元。一个 3 英寸的银立方体价值多少？

(A) $300 $300

(B) $375 $375

(D) $560 $560

(E) $675 $675

Answer

Correct choice: (E)

正确答案：（E）

Solution

Answer (E): The volume of a two-inch cube is $2^3=8$ cu. inches, while that of a three-inch cube is $27$ cu. inches. Therefore, the weight and value of the larger cube is $\frac{27}{8}$ times that of the smaller. \$200$\left(\frac{27}{8}\right)$ = \$675. Note: The actual weight of the cubes is not needed to solve the problem.

答案（E）：边长为2英寸的立方体体积为 $2^3=8$ 立方英寸，而边长为3英寸的立方体体积为 $27$ 立方英寸。因此，大立方体的重量和价值是小立方体的 $\frac{27}{8}$ 倍。 \$200$\left(\frac{27}{8}\right)$ = \$675。注：解决该问题不需要知道立方体的实际重量。

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