Each edge of a cube is increased by 50%. What is the percentage increase in…

Concept: The volume of a cube is (edge)3. If every edge is scaled by a factor k, the volume is scaled by k3 — the percentage increase in volume is NOT the same as the percentage increase in a single edge, because all three dimensions grow together.

Application:

1. Let the original edge be a, so the original volume is a3.

2. The edge increases by 50%, so the new edge is 1.5a.

3. The new volume is (1.5a)3 = 1.53 × a3 = 3.375a3.

4. The increase in volume is 3.375a3 − a3 = 2.375a3, which is 237.5% of the original volume.

Cross-check: Volume is the product of three equal edge-multipliers (each up 50%). Using the successive percentage-change formula: [(1+0.5)(1+0.5)(1+0.5) − 1] × 100 = (3.375 − 1) × 100 = 237.5%, confirming the result.