If the height is doubled in the volume problem (length 4, width 3, original volume 72), what is the new volume?

If the height is doubled in the volume problem (length 4, width 3, original volume 72), what is the new volume?

• A. 72
• B. 108
• C. 144
• D. 216

Answer: (C)

Volume scales with each linear dimension, so changing one dimension while keeping the others fixed changes the volume in proportion to that dimension. Here, length and width stay the same, so doubling the height doubles the volume. From the given, the original volume is 72. Doubling the height gives a new volume of 72 × 2 = 144. Equivalently, 4 × 3 × (2 × 6) = 4 × 3 × 12 = 144.

Volume scales with each linear dimension, so changing one dimension while keeping the others fixed changes the volume in proportion to that dimension. Here, length and width stay the same, so doubling the height doubles the volume. From the given, the original volume is 72. Doubling the height gives a new volume of 72 × 2 = 144. Equivalently, 4 × 3 × (2 × 6) = 4 × 3 × 12 = 144.