Surface area change when cube edge increases by 50%: If each edge of a cube is increased by 50%, by what percentage does the surface area increase?

Introduction / Context:Surface area scales with the square of the linear factor. Increasing each edge by 50% means the linear scale factor is 1.5. Square it to get the area factor, then convert to percentage increase.

Given Data / Assumptions:

• Scale factor k = 1.5
• Area factor = k^2 = 2.25

Concept / Approach:Percentage increase = (area factor − 1) * 100% = (2.25 − 1) * 100% = 125%.

Step-by-Step Solution:k = 1 + 0.5 = 1.5k^2 = 2.25Increase = 2.25 − 1 = 1.25 → 125%

Verification / Alternative check:Let original side be s; new side = 1.5s. Original area = 6s^2; new area = 6*(1.5s)^2 = 6*2.25s^2 = 13.5s^2, which is 125% more than 6s^2.

Why Other Options Are Wrong:50% and 75% reflect linear or partial scaling; 100% would be doubling; 150% is an overestimate (area factor 2.5, not applicable here).

Common Pitfalls:Applying 50% directly to area; forgetting to square the linear factor for area changes.

Final Answer:125 %