Question

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

$\$300$

$\$375$

$\$450$

$\$560$

$\$675$

Answer: E

Concepts:volume power scaling of length, area, and volume

Difficulty rating: 1380

Solution:

The two-inch cube consists of $2^3 = 8$ unit cubes. Each of these unit cubes is worth $200 \div 8 = 25$ dollars. To form a three-inch cube, you need $3^3 = 27$ unit cubes. This means that it is worth $25 \cdot 27 = 675$ dollars.

Thus, E is the correct answer.

1997 AMC 8 Problem 22

Answer: E

Difficulty rating: 1380

Solution:

Problem 22 in Other Years