A solid metal cube weighs 6 pounds. Another cube of the same metal has side length exactly twice as long as the first cube. What is the weight of this larger cube?

Introduction / Context:
This question checks understanding of how volume and mass scale with linear dimensions for three-dimensional shapes. For objects made of the same material, the weight is directly proportional to the volume, provided density remains constant. Here, we compare two metal cubes, where the second cube has twice the side length of the first, and we must determine its weight given the weight of the smaller one.

Given Data / Assumptions:
• Smaller cube weight = 6 pounds. • Larger cube has side length = 2 times the smaller cube. • Both cubes are made of the same metal, so they have the same density. • Weight is proportional to volume.

Concept / Approach:
For a cube, volume V = side^3. If side length is multiplied by a factor k, the volume (and hence weight) is multiplied by k^3. Here, the new side length is twice the original, so k = 2, and the volume factor is 2^3 = 8. Therefore, the weight of the larger cube is 8 times the weight of the smaller cube. We then multiply 6 by 8 to get the new weight.

Step-by-Step Solution:
Step 1: Let the side of the smaller cube be s and its volume be V = s^3. Step 2: The side of the larger cube is 2s, so its volume is (2s)^3. Step 3: Compute (2s)^3 = 2^3 * s^3 = 8 * s^3. Step 4: Therefore, the larger cube has 8 times the volume of the smaller cube. Step 5: Since both cubes are made of the same metal, density is constant, so weight is proportional to volume. Step 6: Weight of larger cube = 8 * (weight of smaller cube) = 8 * 6 = 48 pounds.

Verification / Alternative check:
We can think of the larger cube as being made up of 8 smaller cubes of the original size arranged in a 2 by 2 by 2 pattern. Each smaller cube weighs 6 pounds, and there are 8 such cubes. Multiplying 8 by 6 again gives 48 pounds, confirming the result using a visual volume interpretation.

Why Other Options Are Wrong:
• 12 and 36 do not correspond to an 8-fold increase in weight; 12 is only twice, and 36 is six times the original weight. • 60 would be 10 times the original, which does not match the volume scaling factor 8.

Common Pitfalls:
A frequent error is to think that doubling the side length doubles or quadruples the weight, instead of remembering the cubic relationship. Another mistake is to square the ratio instead of cubing it. Always recall that volumes in three dimensions scale with the cube of the linear factor.

Final Answer:
The weight of the larger cube is 48 pounds.