Each edge of a cube is reduced by 19%. Find the percentage decrease in its total surface area.

Introduction / Context:
Area scales with the square of linear dimensions. If each edge changes by a factor k, total surface area changes by k^2. Here the linear decrease is 19%, so k = 1 − 0.19 = 0.81. We then compute the area factor and translate to a percentage decrease.

Given Data / Assumptions:

• Edge factor k = 0.81.
• Surface area factor = k^2.

Concept / Approach:
Compute k^2 and then determine the decrease: % decrease = (1 − k^2) * 100%. Exact arithmetic avoids rounding issues because 0.81^2 is a standard decimal square.

Step-by-Step Solution:
k^2 = (0.81)^2 = 0.6561Decrease = 1 − 0.6561 = 0.3439 = 34.39%

Verification / Alternative check:
Using percentage compounding: Area decreases by 19% twice (not additive), giving 34.39% overall, consistent with squaring.

Why Other Options Are Wrong:
40% and 35% are rough guesses; 38.4% treats it like 2*19% − (19%)^2/100 but applied to the wrong quantity; only 34.39% correctly squares the linear factor.

Common Pitfalls:
Subtracting 2 * 19% directly (linear thinking) instead of squaring the scale factor; rounding prematurely.

Final Answer:
34.39%